Showing papers in "Journal of the royal statistical society series b-methodological in 1987"

Parameter Orthogonality and Approximate Conditional Inference

Abstract: On propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations, etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

Estimation and Inference by Compact Coding

Abstract: SUMMARY The systematic variation within a set of data, as represented by a usual statistical model, may be used to encode the data in a more compact form than would be possible if they were considered to be purely random. The encoded form has two parts. The first states the inferred estimates of the unknown parameters in the model, the second states the data using an optimal code based on the data probability distribution implied by those parameter estimates. Choosing the model and the estimates that give the most compact coding leads to an interesting general inference procedure. In its strict form it has great generality and several nice properties but is computationally infeasible. An approximate form is developed and its relation to other methods is explored.

Exponential Dispersion Models

Abstract: On etudie les proprietes generales de la classe des modeles de dispersion exponentiels qui est la generalisation multivariable des modeles de distribution d'erreur de Nelder et Wedderburn (1972)

Common Structure of Techniques for Choosing Smoothing Parameters in Regression Problems

Abstract: On tente de relier deux methodes de choix du parametre de lissage, l'une basee sur la mesure du risque et l'autre sur le degre d'ajustement de la regression aux donnees

Chebyshev Polynomial Approximations and Characteristic Function Estimation

Abstract: On developpe une nouvelle procedure pour estimer les fonctions caracteristiques, basee sur un developpement en polynomes de Chebyshev pour la densite du cosinus. Des resultats de simulation confirment l'utilite de la methode

Corrected Maximum Likelihood in Non‐Regular Problems

Abstract: On suggere que l'utilisation du produit des densites pour la fonction de vraisemblance est une mauvaise application de la methode du maximum de vraisemblance dans des cas non reguliers

Affine Invariant Rank Methods in the Bivariate Location Model

Abstract: : The generalized multivariate median of H. Oja is used to define a multivariate notion of quantile, or rank, and to define a measure of scatter of multivariate linear models. The latter, when applied to the one- and two-sample bivariate location models, yields affine invariant analogs of the Wilcoxon rank-sum and signed-rank tests, and of the corresponding estimates. Additional keywords: Dispersion measures; Rank statics. (Author)

Confidence and Conflict in Multivariate Calibration

Abstract: SUMMARY Multivariate calibration involves using an estimated relationship between a multivariate response Y and an explanatory vector X to predict unknown X in future from further observed responses. In controlled calibration with multivariate normal errors, the profile likelihood function for the unknown X (denoted 4) displays a term which measures the mutual inconsistency of the given response vector (denoted Z) in predicting 4. This inconsistency diagnostic fundamentally differentiates the behaviour of likelihood based and Bayes "confidence" regions from those of the unconditional sampling approach. In addition the diagnostic serves to pinpoint an inadequate response vector Z.

Parametric Collapsibility and the Lack of Moderating Effects in Contingency Tables with a Dichotomous Response Variable

Abstract: We consider contingency tables having one variable specified as a response with just two categories. We look at conditions for collapsibility of a symmetric and a directed measure of association, the odds-ratio and the relative risk: situations are discussed under which equal partial associations coincide with the corresponding marginal association. Contrary to the odds-ratio the relative risk is collapsible, if there are independencies in the marginal distribution of the influencing variables. This fact is exploited to derive conditions for the lack of a moderating effect, the latter being a much discussed concept in the social science literature.

Minimum Contrast Estimation for Spectral Densities of Stationary Processes

Abstract: On obtient une large classe d'estimateur efficaces par une methode qui est essentiellement differente du maximum de vraisemblance

Precision, Complexity and Bayesian Model Determination

Abstract: SUMMARY In this paper a new criterion for model determination is proposed. An explicit decision theoretic approach to model selection is employed to derive a Bayes decision rule. The operational characteristics of the criterion are discussed and consistency is shown.

A Note on the Aitkin‐Rubin Approach to Hypothesis Testing in Mixture Models

Abstract: On montre que les conditions de regularite habituellement utilisees pour obtenir des resultats asymptotiques standards ne conviennent pas, meme en utilisant une distribution a priori sur le vecteur des proportions de melange

Cross-Validation Shrinkage of Regression Predictors

Abstract: SUMMARY Copas (1983) suggests that shrinkage of predictors can be related to the least squares slope of actual on predicted values in a new set of data. Considering multiple regression in a cross-validatory setting, this shrinkage slope is approximated by an estimable function of the fitted residuals. Patterns of heteroscedasticity of residual variance can lead to more, or less, shrinkage of least squares. A new predictor using a non-parametric shrinkage multiplier is proposed.

Asymptotic Posterior Normality for Stochastic Processes Revisited

Abstract: The problem of demonstrating the limiting normality of a posterior distribution arising from some stochastic process is revisited. It is shown that certain processes of practical interest are not covered by conditions currently available in the literature. In this paper we present a fairly general set of conditions for asymptotic posterior normality which cover a wide class of problems. The theory is applied to a nonhomogeneous Poisson process and birth process. case of independent and identically distributed (i.i.d.) observations, we mention Le Cam (1953, 1958), Freedman (1963), Lindley (1965), Bickel and Yahav (1969), Walker (1969), Johnson (1970), Dawid (1970), Strasser (1976) and Hartigan (1983). Markov processes, and stochastic processes more generally, are discussed in Borwanker et al (1971), Moore (1976), Heyde and Johnstone (1979), Basawa and Rao (1980) and Chen (1985). The present paper is in the spirit of Heyde and Johnstone (1979), hereafter referred to as H-J, where asymptotic posterior normality is obtained for general stochastic processes under certain conditions. These conditions however do not cover some cases of practical interest; they fail for example for certain nonhomogeneous Poisson processes which are of interest in reliability. We prove here a general result on asymptotic posterior normality which covers a wide class of problems, in particular the type of nonhomogeneous process not covered in the literature. In Section 2 we state our regularity conditions and the main result. We have specialized to the case of a single parameter for reasons of clarity and comparison with existing results. Under the regularity conditions imposed by H-J, it appears that asymptotic posterior normality holds under weaker conditions than those needed for asymptotic normality of the maximum likelihood (ML) estimator. However, a weakening of H-J's conditions, in order to cover a broader range of applications, necessitates the introduction of other conditions which also guarantee the asymptotic normality of the ML estimator. From this point of view, then, it appears that further conditions are needed for posterior normality, since nonlocal, as well as

Identification of Nonzero Elements in the Polynomial Matrices of Mixed Varma Processes

Abstract: On presente des methodes pour identifier des elements non nuls dans des modeles VARMA (1,1) et on montre comment utiliser ces procedures pour construire des modeles d'ordre superieur

Penalized Likelihood Estimation of Hazard and Intensity Functions

Abstract: SUMMARY A non-parametric estimate is proposed for the hazard function using penalized likelihood methods. The estimate turns out to be a hyperbolic spline function which is continuous with its first derivative discontinuous only at a finite number of points. It always assumes positive values, unlike Anderson and Senthilselvan's (1980) quadratic spline estimate. This method is modified for the estimation of the intensity function of a nonstationary Poisson process. An example is given for comparison of the new estimator with the estimator of Anderson and Senthilselvan (1980).

Consistency of Deviance‐Based M Estimators

Abstract: SUMMARY In a general estimation problem, the deviance function generates statistics that are similar to squared standardized residuals. A deviance-based M estimator (DBME) is defined as an adaptively weighted maximum-likelihood estimator, where the weights depend upon the deviances. In both a single-parameter and a regression setting, we give some general conditions under which a DMBE is consistent. For a suitable weighting scheme, these conditions are satisfied in many continuous Cramer-Rao-regular families and in related linear or nonlinear regression cases. The conditions fail (and the estimator is inconsistent) in most discrete families.

Adjustments for kurtosis in factor analysis with elliptically distributed errors

Abstract: On donne des corrections simples aux tests d'ajustement de la theorie normale pour le modele d'analyse factorielle, dans le cas ou les facteurs communs ont des distributions arbitraires et ou les erreurs ont une distribution de la classe elliptique

Statistical Models of Chemical Kinetics in Liquids

Abstract: Statistical methods are used increasingly in theoretical chemistry. Applications range from the use of stochastic relaxation techniques in determining minimum energy molecular configurations to dynamical Monte Carlo simulations of molecular motion in liquids. This paper focuses on diffusion-controlled reactions in radiation chemistry. Here the interest is in describing the evolution of isolated clusters, containing a few chemically active particles, resulting from the passage of ionising radiation through a liquid. The subsequent chemistry is determined by the rate at which the particles can encounter each other, pairwise, in the course of random motion. Classically the trajectories of the particles are described as sample paths of a continuous stochastic process, which in many cases can be assumed to be a diffusion. We have devised an approximate theory based on the approximation that pair distances evolve independently. The effect of this geometric distortion has been studied for small systems by simulation. The extension of this work to a wider class of realistic chemical processes poses many problems. Analytical progress is difficult and methods of simulating large spatial systems are not well developed. Problems which remain to be solved relate to the random geometry of the cluster as its constituent particles diffuse, the development of good approximations to first passage time distributions for diffusions with inhomogeneous drift and methods for the analysis of random motion in a liquid on the basis of detailed non-Markovian models of molecular movement.

On Posterior Asymptotic Normality and Asymptotic Normality of Estimators for the Galton‐Watson Process

Abstract: On etend un resultat de Heyde (1979) et on donne une approche equivalente dans un cadre non bayesien

Estimates for a Regression Parameter Using Ranks

Abstract: On considere une technique de reechantillonnage de Monte Carlo due a Doksum et plusieurs modifications de celle-ci

Some prediction properties of balanced half-sample variance estimators in single-stage sampling

Abstract: On introduit un modele de prediction et une classe d'estimateurs qui inclut plusieurs estimateurs du ratio, de la regression et autres. On donne une approximation a l'estimateur BHS (balanced half-sample)

On the bootstrap and continuity correction

Abstract: On propose une correction de continuite utile lorsque le bootstrap est utilise pour approcher des distributions de moyennes d'echantillons a valeurs sur un treillis

On circuits and optimality conjectures for block designs

Abstract: On montre que la conjecture 5 de John et Williams (1982) implique une condition forte sur les nombres de circuits dans le graphe de concurrence d'un plan binaire A optimal

Two-sample problem with bivariate exchangeable observations

Abstract: On utilise la propriete de symetrie de ce type de probleme et on propose une maniere alternative d'analyser les donnees

Nonparametric Analysis of Covariance with Ordered Alternatives

Abstract: On considere deux statistiques de test: une statistique de Quade generalisee pour k arbitraire et la statistique de Terpstra-Jonckhure generalisee pour des donnees groupees