Showing papers in "Canadian Journal of Statistics-revue Canadienne De Statistique in 1988"

Bootstrap and other methods to measure errors in survey estimates

Abstract: Variance estimation techniques for nonlinear statistics, such as ratios and regression and correlation coefficients, and functionals, such as quantiles, are reviewed in the context of sampling from stratified populations. In particular, resampling methods such as the bootstrap, the jackknife, and balanced repeated replication are compared with the traditional linearization method for nonlinear statistics and a method based on Woodruff's confidence intervals for the quantiles. Results of empirical studies are presented on the bias and stability of these variance estimators and on confidence‐interval coverage probabilities and lengths. Copyright

Sampling properties of estimators of the log‐logistic distribution with application to Canadian precipitation data

Abstract: We consider the probability-weighted moment and the maximum-likelihood estimators of two parameters in the log-logistic distribution. Quantile estimators are obtained using both methods. The distributional properties of these estimators are studied in large samples, via asymptotic theory, and in small and moderate samples, via Monte Carlo simulation. The distribution is shown to be appropriate for a wide variety of meteorological data.

A product-limit estimator for use with length-biased data

Abstract: The following life-testing situation is considered. At some time in the distant past, n objects, from a population with life distribution F, were put in use; whenever an object failed, it was promptly replaced. At some time τ, long after the start of the process, a statistician starts observing the n objects in use at that time; he knows the age of each of those n objects, and observes each of them for a fixed length of time≪ ∞, or until failure, whichever occurs first. In the case where T is finite, some of the observations may be censored; in the case where T =∞, there is no censoring. The total life of an object in use at time ∞ is a length-biased observation from F. A nonparametric estimator of the (cumulative) hazard function is proposed, and is used to construct an estimator of F which is of the product-limit type. Strong uniform consistency results (for n ∞) are obtained. An “Aalen-Johansen” identity, satisfied by any pair of life distributions and their (cumulative) hazard functions, is used in obtaining rate-of-convergence results. On considere la situation suivante dans le contexte des tests de duree de vie. Dans le passe lointain on a mis en fonction n objets d'une population. Leur duree de vie ont F pour fonction de repartition. Chaque fois qu'un objet tombait en panne on le remplacait immediatement. Au moment τ, longtemps apres le debut du processus, un statisticien commence a observer les n objets qui sont en fonction a ce moment-la; il connait l'âge de chacun de ces n objets et observe chacun d'entre eux durant une periode de temps fixee,≪ ∞, ou jusqu'a ce qu'ils tombent en panne. Si T est fini certaines observations peuvent etre censurees. On propose un estimateur nonparametrique de la fonction de hasard (cumulative). Cet estimateur est utilise pour construire un estimateur de F du type “product-limit”. On obtient une convergence uniforme forte. Une identite de “Aalen-Johansen”, qui est satisfaite par toute paire formee d'une fonction de repartition et de sa fonction de hasard (cumulative), est utilisee pour obtenir les resultats sur la vitesse de convergence.

A comparison of regression models for ordinal data in an analysis of transplanted-kidney function

Abstract: Three regression models for ordinal data, those of Fienberg, McCullagh, and Anderson, are applied to an analysis of kidney function among transplant recipients. The conclusions arising from each model are presented and contrasted. On applique trois modeles de regression pour des donnees ordinales afin d'analyser le fonctionnement du rein chez des personnes qui ont re¸u une greffe renale. Les trois modeles considered sont, respectivement, le modele de Fienberg, de McCullagh et de Anderson. Les conclusions auxquelles on arrive a partir de chaque modele sont presentees et comparees.

From the inside out and the outside in: Combining experimental and sampling structures

Abstract: The three basic tenets of experimental design (randomization, replication, local control) find parallels in sampling design. While the ways these parallel structures are applied differ across the two areas, the commonalities suggest ways of strengthening work in both. We describe examples of embedding sampling within experiments, the use of experimental design structures within sample surveys (including interpenetrating networks of samples), and the generalization from experiments to populations through random selection and sampling. A more complicated connecting structure between experiments and surveys is illustrated by the U.S. Census Bureau model for nonsampling errors. We conclude with a description of alternative approaches to basic inference in complicated embedded structures.

Estimating the variance of raking‐ratio estimators

Abstract: This paper is concerned with the asymptotic properties of the converged solution of the raking-ratio estimator. After a description of the raking-ratio estimation procedure, we show that the estimator can be unbiased in the presence of nonresponse if the nonresponse has a particular structure. We also give the asymptotic variance of the estimator. Finally, the results of two numerical applications are presented. Cet article s'interesse aux proprietes asymptotiques de la solution apres convergence de l'estimateur par le quotient obtenu par ratissage. Apres avoir decrit la procedure de ratissage et l'estimateur qui en decoule, nous montrons que ce dernier peut etre sans biais en presence de non-reponse si la non-reponse admet une structure particuliere. Nous fournissons egalement la variance asymptotique de l'estimateur. Finalement, nous presentons les resultats de deux applications numeriques.

Determination of anaerobic threshold

Abstract: This report describes the estimation of the parameters for a model of ventilation (y) by human subjects as a two-segment linear function of oxygen uptake (x). Experimental data were supplied by R.L. Hughson of the Department of Kinesiology. The analysis of one of nine available sets of data is described in detail. Ce rapport decrit l'estimation de parametres associes a un modele de ventilation pulmonaire (y) par des sujets humains ou celle-ci est vue comme une fonction lineaire, segmentee en deux parties, de la prise d'oxygene (x). Les donnees ont ete fournies par le Dr. R.L. Hughson du departement de kinesiologie. L'analyse de l'un des neuf ensembles de donnees disponibles est decrite en detail.

Exponential models, brownian motion, and independence†

Abstract: Some examples of steep, reproductive exponential models are considered. These models are shown to possess a τ-parallel foliation in the terminology of Barndorff-Nielsen and Blaesild. The independence of certain functions follows directly from the foliation. Suppose X(t) is a Wiener process with drift where X(t) = W(t) + ct, 0 < t < T. Furthermore let Y = max [X(s), 0 < s < T]. The joint density of Y and X = X(T), the end value, is studied within the framework of an exponential model, and it is shown that Y(Y – X) is independent of X. It is further shown that Y(Y – X) suitably scaled has an exponential distribution. Further examples are considered by randomizing on T. Dans cet article on considere quelques exemples de modeles exponentiels reproductifs, au sens de Barndorff-Nielsen et Blaesild; ce sont tous des modeles avec un feuilletage τ-parallele, ce qui entraine l'independance de certains couples de variables aleatoires. Soit X(t) = W(t) + ct, 0 < t < T, un processus de Wiener avec derive (“drift”), et soit Y = sup0 < s < T X(s). Alors, la densite conjointe de Y et de X = X(T) est etudiee pour le cas exponentiel. II s'avere que X est independante de Y(Y – X). On montre aussi que la loi de Y(Y – X) est exponentielle apres normalisation. On engendre d'autres exemples en considerant T aleatoire.

Bayesian nonparametric smoothers for regular processes

Abstract: This report is about the analysis of stochastic processes of the form R = S + N, where S is a “smooth” functional and N is noise. The proposed methods derive from the assumption that the observed R-values and unobserved values of R, the assumed inferential objectives of the analysis, are linearly related through Taylor series expansions of observed about unobserved values. The expansion errors and all other priori unspecified quantities have a joint multivariate normal distribution which expresses the prior uncertainty about their values. The results include interpolators, predictors, and derivative estimates, with credibility-interval estimates automatically generated in each case. An analysis of an acid-rain wet-deposition time series is included to indicate the efficacy of the proposed method. It was this problem which led to the methodological developments reported in this paper. Dans cet article, on s'interesse a l'analyse des processus stochastiques de la forme R = S + N, ou S est une fonctionnelle “reguliere” et N est un bruit. Les methodes proposees ici decoulent du presuppose que les valeurs observees de R et ses valeurs non observees, qui sont en fait les objectifs de l'inference dans cette analyse, sont en relation lineaire par l'existence de developpements en series de Taylor des valeurs observees autour des valeurs inobservees. Les termes d'erreur dans ces developpements et toute autre quantite non specifiea priori possedent une distribution multinormale qui reflete l'incertitude qu'on peut avoir a priori en ce qui a trait a leurs valeurs. Les resultats obtenus comprennent des estimateurs en interpolation, des estimateurs previsionnels et des estimateurs en de parametres ayant la forme de derivees, produisant automatiquement dans chaque cas des estimateurs par intervale de credibilite. l'analyse d'une serie chronologique se rapportant aux depots liquides de pluies acides est incluse afin d'illustrer l'efficacite de la methode propose. C'est l'etude de ce probleme particulier qui a donne lieu aux developpements methodologiques decrits dans le present article.

A look at response errors in the Labour Force Survey

Abstract: In conducting surveys, survey-takers impose upon respondents certain cognitive and perceptual tasks the difficulty of which will depend upon a variety of factors. This paper examines the types of questions asked in the Canadian Labour Force Survey with an eye to assessing their "difficulty" and to identifying covariates of difficulty, with respect to both the nature of the information sought and the circumstances of the reinterview. The conclusions are extended to retrospective surveys, where response errors often lead to estimates that are seriously biased.

A model for generalized edit and imputation of survey data

Abstract: The concept of generalized systems for survey processing has gained importance in recent years because of resource constraints. Statistics Canada has adopted a policy to develop generalized systems to the extent that is feasible and cost-efficient. A generalized edit and imputation (E&I) system is of prime importance. An E&I system is proposed that describes the overall edit and imputation function as comprising five component functions: edit specification, edit analysis, edit application, error localization, and imputation. Implementation of the E&I model, especially for numerical data, is discussed. The focus is on methodology rather than systems. L'idee de systemes generalises pour le traitement d'enquetes a pris de l'importance au cours des dernieres annees a cause de la limitation des ressources. Statistique Canada a adopte une politique de developpement de systemes generalises qui est faisable sans etre excessivement couteuse. Un systeme generalise de controle et d'imputation est primordial. Nous en proposons un qui englobe cinq composantes dans sa fonction de controle et d'imputation; elles sont respectivement la specification, l'analyse et l'application, pour ce qui est du controle, la localisation des erreurs et l'imputation elle-meme. Nous etudions l'utilisation de ce modele de controle et d'imputation, particulierement pour le traitement de donnees numeriques. L'accent est plutot mis sur l'aspect methodologique qu'informatique.

The variability of rainfall acidity revisited

Abstract: Six years of rainfall-event pH measurements from the nine-station MAP3S/PCN monitoring network in the eastern United States were analyzed. The initial objective was an attempted validation of the model developed by Eynon and Switzer (1983, Canad. J. Statist. 11, 11–24) on this independent data set. Because some features of the structure presumed in the model are not evident in this data set, the underlying structure of the data was then explored in some detail. Both aspects of the investigation confirmed that the identification of an appropriate statistical model for such data is a difficult undertaking; anticipated structure may not be evident, and the data corresponding to specific stations or years may exhibit anomalous behavior. Nous avons analyse six annees de mesures se rapportant au pH de pluie, mesures qui ont ete prelevees aux neuf stations du reseau de detection MAP35/PCN de l'est des Etats-Unis. Nous avions comme objectif initial de tenter de voir si le modele developpe par Eynon et Switzer (1983, La Revue Canadienne de Statistique, 11, 11–14) etait valide pour decrire cet ensemble de donnees independant. Mais parce que certaines caracteristiques de la structure presumee par le modele n'etaient pas apparentes dans cet ensemble de donnees, une exploration quelque peu detailles de la structure sous-jacente dec donnees a done ete entreprise. Les deux volets de l'investigation confirment que l'identification d'un modele statistique approprie a de telle donnees constitue une tâche difficile; une structure anticipee peut ne pas etre evidente et les donnees provenant d'une station particuliere au d'une annee particuliere peuvent tres bien comporter des anomalies.

Criteria for the equality between ordinary least squares and best linear unbiased estimators under certain linear models

Abstract: A new necessary and sufficient condition is derived for the equality between the ordinary least-squares estimator and the best linear unbiased estimator of the expectation vector in linear models with certain specific design matrices. This condition is then applied to special cases involving one-way and two-way classification models. Nous nous interessons a l'estimation du vecteur des esperances dans les modeles lineaires comportant des matrices de schema specifiques. Nous formulons une nouvelle condition necessaire et suffisante pour que l'estimateur ordinaire des moindres carres et le meilleur estimateur lineaire sans biais coincident. Par la suite, nous appliquons cette condition a des cas particuliers comprenant les plans a classification simple et a classification double.

Interval estimates for diatom-inferred lake pH histories

Abstract: We investigate ordinary least-squares and Bayesian methods for constructing interval estimates for historical lake pH's inferred from diatom sediments. The Bayesian method explicitly models several forms of variability, including the sampling and classification variability of the diatom records, estimation variability, and measurement error in observed pH's. The two methods produce similar interval estimates, but the Bayesian model allows design recommendations to be made.

Bootstrap variance and bias estimation in linear models

Abstract: Let θ be a nonlinear function of the regression parameters and θ be its estimator based on the least-squares method. This paper studies the bootstrap estimators of the variance and bias of θ. The bootstrap estimators are shown to be consistent and asymptotically unbiased under some conditions. Asymptotic orders of the mean squared errors of the bootstrap estimators are also obtained. The bootstrap and the classical linearization method are compared in a simulation study. Discussions about when to use the bootstrap are given. Soit θ une fonction non-lineaire des parametres de regression et θ son estimateur de moindres carres. Dans cet article on etudie les estimateurs “bootstrap” de la variance et du biais de θ. On montre que, sous certaines conditions, les estimateurs “bootstrap” sont convergents et asymptotiquement sans biais. On obtient aussi l'ordre asymptotique de l'erreur quadratique moyenne des estimateurs “bootstrap”. Dans une etude de simulation, on compare la methode “bootstrap” avec la methode classique de linearisation. On discute des cas ou il est approprie d'employer le “bootstrap”.

Improved shrinkage estimators for the mean vector of a scale mixture of normals with unknown variance

Abstract: The problem of estimating the mean θ of a not necessarily normal p-variate (p > 3) distribution with unknown covariance matrix of the form σ2A (A a known diagonal matrix) on the basis of ni > 2 observations on each coordinate Xt (1 < i < p) is considered. It is argued that the class of scale (or variance) mixtures of normal distributions is a reasonable class to study. Assuming the loss function is quadratic, a large class of improved shrinkage estimators is developed in the case of a balanced design. We generalize results of Berger and Strawderman for one observation in the known-variance case. This methodology also permits the development of a new class of minimax shrinkage estimators of the mean of a p-variate normal distribution for an unbalanced design. Numerical calculations show that the improvements in risk can be substantial. Le probleme concerne l'estimation de la moyenne θ d'une distribution p-dimensionnelle, non necessairement normale, avec matrice de covariances inconnue de la forme σ2A σA est une matrice diagonale supposee connue. Les estimateurs proposes sont bases sur ni > 2 observations pour chaque coordonnee Xi(1 < i < p). Nous justifions d'abord le choix d'une classe de distributions obtenues par melange de lois normales pour etudier le probleme precite. En considerant une fonction de perte quadratique, nous definissons dans le contexte d'un plan d'experience equilibre une grande classe d'estimateurs ameliores du type James-Stein. Nous generalisons ainsi certains resultats de Berger et Strawderman qui se rapportent a une observation avec variance connue. La technique employee permet egalement de developper une nouvelle classe d'estimateurs contractes et minimax pour la moyenne d'une densite normale p-dimensionnelle dans le cas non equilibre. l'evaluation numerique du risque de nos estimateurs illustre leur avantage par rapport aux estimateurs classiques.

Patterned matrix derivatives

Abstract: A general procedure for obtaining matrix derivatives of functions of nonlinear patterned matrices is proposed. The method is extended to obtain the Jacobians of patterned matrix transformations. Nel (1980) and Wiens (1985) consider the linear patterned cases. The procedure proposed here takes care of these cases as well. On propose une methode generate pour obtenir des matrices derivees de fonctions de matrices dont les elements satisfont des relations non-lineaires. La methode est generalisee pour les jacobiens des transformations dont la matrice est du type mentionne plus haut. Nel (1980) et Wiens (1985) ont considere le cas lineaire. La methode presentee permet de traiter ce cas aussi.

A note on L1 consistent estimation

Abstract: Let (, ) be a space with a σ-field, M = {Ps; s o} a family of probability measures on A, Θ arbitrary, X1,…,Xn independently and identically distributed P random variables. Metrize Θ with the L1 distance between measures, and assume identifiability. Minimum-distance estimators are constructed that relate rates of convergence with Vapnik-Cervonenkis exponents when M is “regular”. An alternative construction of estimates is offered via Kolmogorov's chain argument. Soient un espace muni d'une σ-algebre et M = {Ps: s Θ} une famille de mesures de probabilite sur ; Θ est un espace arbitraire. Soient X1,…,Xn des variables aleatoires independantes de měme loi Pθ. Sur Θ, on prend la distance L1 entre les mesures. On construit des estimateurs a distance minimale quand M est un espace «regulier». La vitesse de convergence des estimateurs vers le vrai parametre depend de l'exposant de Vapnik et Cervonenkis. On presente aussi une autre methode de construction des estimateurs qui utilise la technique de la chaǐne de Kolmogorov.

An Explicit Formula for the Risk of the Positive‐Part James‐Stein Estimator

Abstract: When estimating a normal mean vector with variance known up to a multiplicative factor, it is well known that the positive-part James-Stein estimator is not admissible, but until now, no one has been able to exhibit a uniformly better estimator. We propose here an explicit formula for the risk of the positive-part James-Stein estimator. Pour l'estimation de la moyenne d'un vecteur normal dont la variance est connue a un facteur pres, on ne connait pas d'estimateur dominant uniformement l'estimateur de James-Stein tronque, bien que celui-ci ne soit pas admissible. Nous etablissons ici la formule explicite du risque de l'estimateur de James-Stein tronque, generalisant le resultat d'Egerton et Laycock (1982) pour l'estimateur de James-Stein.

The one-way analysis of variance with ordered alternatives: A modification of bartholomew's Ē2 Test

Abstract: Tests of homogeneity of normal means with the alternative restricted by an ordering on the means are considered. The simply ordered case, μ1 ≤ μ2 ≤ ··· ≤ μk, and the simple tree ordering, μ1 ≤ μj, for; j= 2, 3,…, k, are emphasized. A modification of the likelihood-ratio test is proposed which is asymptotically equivalent to it but is more robust to violations of the hypothesized orderings. The new test has power at the points satisfying the hypothesized ordering which is similar to that of the likelihood-ratio test provided the degrees of freedom are not too small. The modified test is shown to be unbiased and consistent. Nous considerons les tests d'homogeneite des moyennes de populations normales lorsque les contre-hypotheses stipulent une relation d'ordre entre celles-ci. Nous insistons davantage sur le cas d'un ordre total, μ1 ≤ μ2 ≤ ··· ≤ μk et sur le cas d'un ordre arborescent, μ1 ≤ μjj = 2, 3, …, k. Nous proposons une modification au test du rapport de vraisemblance qui le rend plus robuste quant aux ecarts a l'ordre specifie par la contre-hypothese. Le nouveau test, qui est asymptotiquement equivalent au test du rapport de vraisemblance, admet aux points qui satisfont a l'ordre specifie une puissance similaire a celle du test du rapport de vraisemblance a condition que les degres de liberte ne soient pas trop faibles. Nous demontrons que le test modifie est sans biais et convergent.

Improved set estimators for the coefficients of a linear model when the error distribution is spherically symmetric with unknown variances

Abstract: The usual confidence set for p (p ≥ 3) coefficients of a linear model is known to be dominated by the James-Stein confidence sets under the assumption of spherical symmetric errors with known variance (Hwang and Chen 1986). For the same confidence-set problem but for the unknown-variance case, naturally one replaces the unknown variance by an estimator. For the normal case, many previous studies have shown numerically that the resultant James-Stein confidence sets dominate the resultant usual confidence sets, i.e., the F confidence sets. In this paper we provide a further asymptotic justification, and we discover the same advantage of the James-Stein confidence sets for normal error as well as spherically symmetric error. On sait que la region de confiance usuelle pour p (p ≥ 3) coefficients d'un modele lineaire est dominee par les regions de confiance du type James-Stein si on suppose la symetrie spherique, avec variance connue, des termes d'erreur (Hwang et Chen 1986). Lorsque la variance est inconnue, la demarche naturelle consiste a remplacer celle-ci par un estimateur. Dans le cas d'observations normales, plusieurs etudes anterieures ont montre numeriquement que les regions de confiance du type James-Stein qui en resultent dominaient les regions de confiance usuelles qui en resultent, a savoir, celles construites a l'aide d'une loi F. Nous fournissons dans cet article une justification asymptotique supplementaire de ce resultat et nous remarquons que les regions de confiance du type James-Stein sont aussi avantageuses, que les termes d'erreur soient normalement distribues ou qu'ils presentent une symetrie spherique.

Two‐moment approximations to some null distributions in order‐restricted inference: Unequal sample sizes

Abstract: Bartholomew's statistics for testing homogeneity of normal means with ordered alternatives have null distributions which are mixtures of chi-squared or beta distributions according as the variances are known or not. If the sample sizes are not equal, the mixing coefficients can be difficult to compute. For a simple order and a simple tree ordering, approximations to the significance levels of these tests have been developed which are based on patterns in the weight sets. However, for a moderate or large number of means, these approximations can be tedious to implement. Employing the same approach that was used in the development of these approximations, two-moment chisquared and beta approximations are derived for these significance levels. Approximations are also developed for the testing situation in which the order restriction is the null hypothesis. Numerical studies show that in each of the cases the two-moment approximation is quite satisfactory for most practical purposes.

Recursive improvement of estimates in a Gauss‐Markov model with linear restrictions

Abstract: The minimum-dispersion linear unbiased estimator of a set of estimable functions in a general Gauss-Markov model with double linear restrictions is considered. The attention is focused on developing a recursive formula in which an initial estimator, obtained from the unrestricted model, is corrected with respect to the restrictions successively incorporated into the model. The established formula generalizes known results developed for the simple Gauss-Markov model. Nous considerons l'estimateur lineaire sans biais a dispersion minimale d'un ensemble de fonctions estimables dans un modele de Gauss-Markov general a double contrainte lineaire. Nous nous concentrons sur le developpement d'une formule de recurrence dans laquelle un estimateur initial est d'abord obtenu du modele sans contrainte, puis corrige de facon a respecter les contraintes qui sont successivement incorporees dans le modele. L'etablissement de cette formule generalise des resultats connus developpes pour le modele de Gauss-Markov simple.

A new look at an old problem: Finding temporal patterns in homicide series—the Canadian case

Abstract: It is believed by criminologists that the incidence of crimes committed against persons is highest in the summer. Knowledge about the annual patterns and other temporal behavior of such crimes can help authorities in prevention. The objective of this study is to reveal the temporal behavior of murders in Canada and assess if they are affected by trend-cyclical and/or seasonal influences. The series analyzed comprise the period 1961 to 1980 and are classified according to suspects and victims. Only the quarterly series display a significant seasonal pattern, with the peak occurring in the third quarter. We have also analyzed the relationship between the trend cycle of the murder series and two other variables, namely unemployment rate and rate of growth of the 15-to-44 age group. Les criminologistes sont d'avis que le nombre de crimes commis contre la personne est plus eleve l'ete. Une telle connaissance des mouvements temporels caracteristiques des series de crime contre la personne peut contribuer a la prevention de tels crimes. Le but de cette etude est justement de deceler la presence et d'estimer des mouvements temporels tels la saisonnalite et la tendance-cycle dans les series de meurtres au Canada. Les series a l'etude qui vont de 1961 a 1980 sont classees en deux grandes categories, les suspects et les victimes. Seules les series trimestrielles ont revele une saisonnalite significative tout particulierement au troisieme trimestre. Nous avons egalement analyse la relation qui existe entre la tendance-cycle de la serie de meurtres au Canada le taux de chomage et l'evolution demographique du groupe d'âge 15–44 ans.

Optimum invariant tests for random manova models

Abstract: Consider the canonical-form MANOVA setup with X: n × p = (+ E, Xi ni × p, i = 1, 2, 3, Mi: ni × p, i = 1, 2, n1 + n2 + n3) p, where E is a normally distributed error matrix with mean zero and dispersion In (> 0 (positive definite). Assume (in contrast with the usual case) that M1i is normal with mean zero and dispersion In1) and M22 is either fixed or random normal with mean zero and different dispersion matrix In2 (being unknown. It is also assumed that M1E, and M2 (if random) are all independent. For testing H0) = 0 versus H1: (> 0, it is shown that when either n2 = 0 or M2 is fixed if n2 > 0, the trace test of Pillai (1955) is uniformly most powerful invariant (UMPI) if min(n1, p)= 1 and locally best invariant (LBI) if min(n1p) > 1 underthe action of the full linear group Gl (p). When p > 1, the LBI test is also derived under a somewhat smaller group GT(p) of p × p lower triangular matrices with positive diagonal elements. However, such results do not hold if n2 > 0 and M2 is random. The null, nonnull, and optimality robustness of Pillai's trace test under Gl(p) for suitable deviations from normality is pointed out. Considerons la forme canonique du modele d'analyse de variance multivariee ou X: n × p = (E, Xi × ni × p, i = 1, 2, 3, Mi: ni × p, i = 1, 2, n1 + n2 + n3) p, ou E est une matrice de termes d'erreur de loi multinormale avec moyenne nulle et dispersion In (> 0 (definie positive). Contrairement au cas classique, supposons que M1 admette une loi multinormale de moyenne nulle et dispersion In1) que M2 soit, ou bien fixe, ou bien de loi multinormale avec moyenne nulle et dispersion In2 (et) etant inconnues. Supposons egalement que M1M2 (si aleatoire) et E soient mutuellement independantes. Nous desirons confronter les hypotheses H0: (= 0 et H1) 0. Nous montrons que, lorsque n2 = 0 ou lorsque M2 est fixe si n2 > 0, le test de la trace de Pillai (1955) est le test invariant uniformement le plus puissant (IUPP) si min (n1 p)= 1 et localement le plus puissant (ILPP) si min (n1p) > 1 sous ľaction du groupe lineaire complet Gl(p). Lorsque p > 1, nous construisons egalement le test ILPP mais sous l'action d'un groupe plus restreint, a savoir, le groupe Gr(p) des matrices triangulaires inferieures p × p ne comportant que des elements positifs sur la diagonale. Toutefois, de tels resultats ne tiennent plus lorsque n2 > 0 et M2 est aleatoire. Enfin, nous faisons etat de la robustesse du test de la trace de Pillai sous Gl(p) quant a ses lois de probabilite sous les deux hypotheses et quant a son optimalite lorsque la loi qui regit les observations s'ecarte de la normale.

On the Simultaneous Estimation of Scale Parameters

Abstract: This note is an extension of Das Gupta's results (1986) on the estimation of multiparameter gamma distribution. Consider p (p ⩾ 2) independent positive random variables with possibly different scale-parameter densities. For the estimation of the powers of the scale parameters it is shown that the “best multiple estimator” is inadmissible with respect to a large class of weighted quadratic loss functions. Cette note generalise un resultat de Das Gupta (1986) sur l'estimation simultanee de parametres d'echelle provenant de lois gamma independantes. On considere p (p ⩾ 2) variables aleatoires positives et independantes avec, peut-etre, differentes densites contenant un parametre d'echelle. Pour l'estimation des puissances des parametres d'echelle on demontre que le “meilleur multiple estimateur” est inadmissible pour une grande classe de fonctions de perte quadratiques ponderees.

Is statistics singular or plural

Abstract: It is the theme of the paper that statistics as a body of data are vastly more useable and useful when statistics as a discipline underlies or guides their collection and exploitation. While this statement might, in the abstract, be accepted by the profession, the extent to which it is practised can substantially be improved. Within this broader context the paper focuses on the role of statistical analysis, identifies and discusses different types of analytical activities, explores both the significance of analytical activities for official statistical agencies and the necessary restrictions on such agencies' analytical activities. It concludes by arguing in favour of more data analytical work both by academic personnel and staff of official statistical agencies and provides examples of how such work would enhance the real, as well as the perceived, value of statistics. Le present article a pour theme que les statistiques sont beaucoup plus pratiques et utiles lorsque leur collecte et leur exploitation sont fondees sur les concepts et methodes de la statistique. Les milieux professionnels peuvent etre dans l'abstrait d'accord avec cette idee, mais il demeure que celle-ci pourrait etre beaucoup plus mise en pratique. Dans ce contexte general, les auteurs traitent surtout du role de l'analyse statistique, examinent les differents types d'activite analytique, et etudient a la fois l'importance des activites analytiques pour les organismes statistiques officiels et les limites qu'il faut fixer a ces activites. Ils concluent en soulignant que les milieux specialises et le personnel des organismes statistiques officiels doivent l'un comme l'autre realiser davantage de travaux d'analyse des donnees, et ils donnent des exemples illustrant comment ces travaux pourraient permettre d'ameliorer la valeur reelle des statistiques de meme que l'idee que l'on se fait d'elles. Mots cles: statistique, analyse statistique, statistiques officielles.

Comparing and testing order relations between percentile residual life functions

Abstract: We consider the problem of comparing and testing order relations between percentile residual life functions. We introduce R-R plots and processes and develop a general approach for this problem. Dans cet article on considere le probleme de comparer et de tester des relations d'ordre entre des fonctions de percentiles liees aux durees de vie residuelles. On introduit des representations du type R-R et on developpe une approche generate pour ce probleme.

Dessaisonalisation d'un tableau avec contraintes linéaires: Application aux flux financiers canadiens

Abstract: Canadian financial flows represent a detailed set of time series, satisfying a number of accounting identities. When seasonal adjustments are made using the X-11-ARIMA program, the original linear constraints no longer hold. This article introduces a procedure that recovers consistency for seasonally adjusted financial flows. A weighted least squares minimization method is used to change as little as possible the individually seasonally adjusted financial flow series. Results pertaining to a restricted set of Canadian financial flows are presented. Les flux financiers canadiens representent un ensemble detaille de series chronologiques obeissant a des identites comptables. Lorsqu'on dessaisonalise individuellement en utilisant X-11-ARMMI, les relations lineaires originales ne sont plus respectees. Cet article presente donc une procedure pour recreer un tableau coherent des flux financiers apres dessaisonalisation. La methode de minimisation des moindres carres ponderes est preconisee dans cette etude, afin d'affecter le moins possible les series des flux financiers dessaisonalisees individuellement. Des resultats sont presentes pour un ensemble restreint des flux financiers canadiens.

Strong approximations of quadratic sums of uniform spacings

Abstract: We obtain a strong approximation for the quadratic sum process of uniform spacings. Nous obtenons une approximation forte du processus des sommes quadratiques d'accroissements uniformes.