Showing papers in "Journal of the royal statistical society series b-methodological in 1988"

Kernel smoothing in partial linear models

Abstract: On considere deux methodes d'estimation: l'une reliee aux splines de lissage partiels, l'autre motivee par une analyse de residus partielle

Estimation and model identification for continuous spatial processes

Abstract: SUMMARY Formal parameter estimation and model identification procedures for continuous domain spatial processes are introduced. The processes are assumed to be adequately described by a linear model with residuals that follow a second-order stationary Gaussian random field and data are assumed to consist of noisy observations of the process at arbitrary sampling locations. A general class of two-dimensional rational spectral density functions with elliptic contours is used to model the spatial covariance function. An iterative estimation procedure alleviates many of the computational difficulties of conventional maximum likelihood estimation for non-lattice data. The procedure is applied to several generated data sets and to an actual ground-water data set.

Binary Regression Models for Contaminated Data

Abstract: On etudie la nature des observations aberrantes dans le contexte des donnees de regression binaires. On propose un modele simple qui permet qu'un petit nombre de reponses binaires soit mal enregistre

A Review of Bootstrap Confidence Intervals

Abstract: On passe en revue plusieurs methodes distinctes basees sur le bootstrap pour construire des intervalles de confiance

On the Distribution of a Studentized Quantile

Abstract: La variance asymptotique du quantile d'echantillon depend de la valeur de la densite de population et du quantile de la population. On considere l'estimateur de Siddiqui-Bloch-Gastwinth

Variance Function Estimation in Regression: the Effect of Estimating the Mean

Abstract: : The authors consider estimation of a variance function g in regression problems. Such estimation requires simultaneous estimation of the mean function f. We obtain sharp results on the extent to which the smoothness of f influences best rates of convergence for estimating g. For example, in nonparametric regression with two derivatives on g, classical rates of convergence are possible if and only if the unknown f satisfies a Lipschitz condition of order 1/3 or more. If a parametric model is known for g, then g may be estimated n 1/2 - consistently if and only if f is Lipschitz of order 1/2 or more. Optimal rates of convergence are attained by kernel estimators.

On Symmetric Bootstrap Confidence Intervals

Abstract: On montre que dans des circonstances generales les intervalles de confiance du bootstrap de percentile t symetrique ont une erreur de recouvrement O(n −2 ) ou n denote la taille d'echantillon

Approximate conditional inference in generalized linear models

Abstract: On developpe des approximations precises et facilement calculables pour les densites conditionnelles et les distributions des statistiques exhaustives dans les modeles lineaires generalises avec des fonctions de liaison canoniques

Quantifying Expert Opinion in Linear Regression Problems

Abstract: SUMMARY This paper describes a method for choosing a natural conjugate prior distribution for a normal linear sampling model. A person using the method to quantify his/her opinions performs specified elicitation tasks. The hyperparameters of the conjugate distribution are estimated from the elicited values. The method is designed to require elicitation tasks that people can perform competently and introduces a type of task not previously reported. A property of the method is that the assessed variance matrices are certain to be positive definite. The method is sufficiently simple to implement with an interactive computer program on a microcomputer. Bayesian statistical methods provide a formal mechanism for taking into account prior knowledge, meaning information available 'prior' to the statistical data to be analysed. In many circumstances, prior knowledge is based on historical data that are only recorded in the form of the personal experience of experts. To use the information, the expert must quantify his/her opinions, by answering comprehensible questions concerning unknown but definite quantities of direct interest. His set of answers should enable a probability distribution to be determined. This distribution must satisfy the usual laws of probability so that, for example, any variance-covariance matrix must be positive definite. In addition, the distribution should be 'accurate' in some sense. For example, the distribution might be required to describe the expert's knowledge closely or, perhaps, to predict subsequent events with relative success. The accuracy of the assessed distribution will depend, in part, on the method of elicitation. In this paper we present a method of assessing a subjective prior distribution for a normal linear sampling model. This is an important task, owing to the wide applicability of such models and the many situations where expert personal opinion could be used more efficiently, communicated more accurately and judged more critically if it were available in a suitable form. We denote a particular setting of the independent variables by x and the dependent variable by y, referring to the former as a design point and the latter as the response. The model specifies that the 'objective' or 'sampling' distribution of y, conditional on x and the sampling model parameters

A Note on Extended Quasi-Likelihood

Abstract: : We study the method of extended quasi-likelihood estimation and inference of a variance function recently proposed by Nelder & Pregibon (1987). The estimates are inconsistent in general, and the test levels can be biased, but in many cases such as the exponential family the inconsistency and bias will not be a major concern. Extended quasi-likelihood is compared with Carroll & Ruppert's (1982) pseudo-likelihood method, which gives consistent estimates and, when slightly modified, asymptotically unbiased tests. We quantify the showing in this instance that the two estimates are closely related and may be asymptotically equivalent in many important cases. However, in some cases outside the exponential family, an asymptotic bias can persist. Heteroscedastic regression model.

Consistent Estimates for the Near(2) and Nlar(2) Time Series Models

Abstract: On montre qu'il est possible d'utiliser des techniques similaires a celles de Nicholls et Quinn (1982) pour obtenir des estimateurs consistants et asymptotiquement normaux pour les quatre parametres des modeles NEAR (2) et NLAR (2) introduits par Lawrance et Lewis (1985)

Symmetry models and hypotheses for structured data layouts

Abstract: On peut utiliser des proprietes de symetrie pour deriver des tests valides d'hypotheses nulles et pour construire des modeles statistiques appropries pour les donnees. On developpe des idees generales et on les illustre dans le contexte d'une classification a deux criteres

Limit Distribution of a High Order Markov Chain

Abstract: On obtient la distribution limite d'une chaine de Markov d'ordre k>1 sous des conditions plus faibles que celles supposees par Raftery (1985)

Does Simple Random Sampling Provide Adequate Balance

Abstract: Une etude empirique montre que sous un echantillonnage aleatoire simple les intervalles de confiance du total peuvent avoir des probabilites de recouvrement conditionnelles qui sont imposantes de facon persistante lorsque la taille de l'echantillon croit

Adjusting Belief Structures

Abstract: On suggere une approche dans laquelle les enonces de croyance sont organises en structures de croyance qui sont ajustees par l'observation sur des structures de croyance associees et on derive les proprietes de tels ajustements

Bayes methods for outliers in exponential samples

Abstract: On presente une approche bayesienne a la modelisation des observations aberrantes et on l'examine en relation avec les membres de la famille exponentielle en general et avec la distribution exponentielle en particulier

Consistent Order Determination for Processes with Infinite Variance

Abstract: SUMMARY Order determination for autoregressive processes when the residuals have a distribution belonging to the domain of attraction of an infinite variance stable law is examined. The use of the FPE, criterion of Bhansali and Downham (1977) is shown to provide a consistent estimator of the order with any a > 0. Order determination for moving average processes is considered; a procedure based on autoregressive estimates of the inverse correlations, see Bhansali (1983), is shown to provide a consistent estimator of the order. Consistency of the estimated autoregressive and moving average parameters of an arbitrary order is established. The question of consistent discrimination between autoregressive and moving average models is also considered. The finite sample behaviour of the discrimination procedure is investigated by means of a simulation study.

Saddlepoint Expansions for Directional Test Probabilities

Abstract: An expansion is derived for the conditional tail probability of a multivariate random variable given its direction from the expected value. In particular, if the score function of a statistical model is chosen as this variable, such a conditional probability gives a test for a simple hypothesis, which is asymptotically equivalent to the likelihood ratio test. The expansion is of the large deviation type and is derived through the use of saddlepoint methods. Thus the relative error of the test probability is O(n1) uniformly in a bounded set for an average of n independent replications. The approximation is based on the cumulant transform for the random variable, but is otherwise a simple expression in terms of chi-squared distributions. In the one-dimensional case it reduces to the expansion obtained by Lugannani and Rice. Numerical examples show an excellent fit, comparable with other saddlepoint expansions, when the dimension is low, even for very small sample sizes, but for higher dimensions more replications are required to give a similar approximation.

Gittins procedures for bandits with delayed responses

Abstract: This paper introduces the multi-armed delayed response bandit with geometric discounting. The existence of dynamic allocation indices is shown when the discount factor is less than 1/2 or when the information bank size is zero. For the multi-armed delayed response bandit, the arm indicated by the dynamic allocation procedure or Gittins procedure is optimal when all information bank sizes are zero. A computational method for calculating indices is presented. The idea is to approximate the optimal strategy using a class of strategies whose worths are easy to calculate.

A Generalization of a Nonparametric Test for Stochastically Ordered Distributions to Censored Survival Data

Abstract: On definit un nouveau test de tendance qui peut etre vu comme une generalisation du test de regression isotonique de Chako (1963)

Control of Stochastic Loss Networks, with Applications

Abstract: On considere le probleme du controle d'un reseau stochastique de capacite finie qui peut traiter des appels (ou des clients) de differents types avec, comme objectif, la minimisation du cout d'equilibre attendu par unite de temps provenant du rejet de certains appels

Inference from Accelerated Life Tests Using Filtering in Coloured Noise

Abstract: SUMMARY We present a new approach for inference from accelerated life tests. Our approach formulates such problems as inference under Kalman filter models with correlated observation errors. We restrict attention to exponential life distributions, and the power rule as a time transformation function. Extensions to other time transformation functions are straightforward; however, extensions to other distributions involve non-linear filtering and are not considered. The advantages of our formulation are that we are able to incorporate uncertainty in the time transformation function and also are able to allow it to change with the stress. To validate our approach we consider some simulated data; to give it a sense of reality we apply it to actual data.

A Note on the Existence of Maximum Likelihood Estimates in Linear Regression Models Using Interval-censored Data

Abstract: SUMMARY For a class of linear regression models with interval-censored data, including the exponential regression model as a special case, a necessary and sufficient condition is given for the existence of the maximum likelihood estimator (MLE). The condition is especially simple to check for simple linear regression. This result is useful for comparing the small sample properties of MLEs from different special cases of interval-censored data.

Nonparametric Estimation of the Probability of a Long Delay in the M/G/1 Queue.

Abstract: : An M/G/1 queue is approached by stationary Poisson traffic with known arrival rate. Observations of service times are all that is known about the service distribution. Nonparametric estimates of the probability of a long customer delay are given. The estimates include the solution of an equation involving the empirical transform of the service times. Asymptotic properties of the estimates are derived. Simulation studies of the small sample behavior of the estimates are reported. The jackknife is used to provide error assessment of the estimates and to construct confidence intervals in the simulation studies of small sample behavior. Keywords: Asymptotic Normality.

Bahadur efficiency of two-sample tests based on one-sample sign statistics

Abstract: On considere le test de position a deux echantillons base sur la comparaison de deux intervalles de confiance independants de la distribution derives de statistiques de signes

Estimating subgroup means with misclassification

Abstract: On etudie un estimateur simple non iteratif resultant de l'estimateur de Selen (1986) lorsque les probabilites de mauvaise classification sont estimees de facon independante

The efficiency factors of particular effects in designs with orthogonal factorial structure

Abstract: On etudie le confounding partiel qui n'est pas necessairement orthogonal aux blocs. On relie le facteur d'efficacite d'une interaction ou d'un effet principaux aux nombres de chemins d'un certain type dans le graphe de concurrence des traitements