bluuebunny/crossref_metadata_2025 huggingface dataset:
De l'unicité des estimateurs robustes en régression lorsque le paramètre d'échelle et le paramètre de la régression sont estimés simultanément
Authors: Rivest Louis‐Paul
Published: June 2006

Plusieurs méthodes ont été suggérées pour calculer les M et les G‐M‐estimateurs de β, le paramètre de la régression, et de σ, le paramètre d'échelle, dans un modèle linéaire. Cet article montre que, pour quelques jeux de données fameux en statistique robuste, les systèmes d'équations nonlinéaires pour l'estimation simultanée de β, à l'aide d'un M‐estimateur ayant une fonction ψ redescendante, et de σ à l'aide de la médiane des valeurs absolues des résidus, ont plusieurs solutions. Cette multiplicité est causée non pas par la présence d'une fonction ψ redescendante qui fait en sorte que β n'est pas toujours bien défini même si σ est connu, mais bien par l'estimation simultanée de β et de σ. Les difficultés mises en lumière dans ce travail peuvent être évitées en employant une méthode de calcul différente, en deux étapes. On estime d'abord σ à l'aide de la médiane des valeurs absolues des résidus obtenus pour en estimateur robuste défini de façon unique tel le “Proposal 2” de Huber ou l'estimateur basé sur la norme L1. On estime ensuite β en résolvant le système nonlinéaire pour le M‐estimateur oú σ prend la valeur calculée à la première étape. Des conditions analytiques d'unicité pour les M et les G‐M‐estimateurs sont aussi présentées.
Test for the equality of several correlation coefficients
Authors: Paul S. R.
Published: June 2006

We derive two C(α) statistics and the likelihood‐ratio statistic for testing the equality of several correlation coefficients, from k ≥ 2 independent random samples from bivariate normal populations. The asymptotic relationship of the C(α) tests, the likelihood‐ratio test, and a statistic based on the normality assumption of Fisher's Z‐transform of the sample correlation coefficient is established. A comparative performance study, in terms of size and power, is then conducted by Monte Carlo simulations. The likelihood‐ratio statistic is often too liberal, and the statistic based on Fisher's Z‐transform is conservative. The performance of the two C(α) statistics is identical. They maintain significance level well and have almost the same power as the other statistics when empirically calculated critical values of the same size are used. The C(α) statistic based on a noniterative estimate of the common correlation coefficient (based on Fisher's Z‐transform) is recommended.
A multivariate extension of poisson's theorem
Authors: Wang Y. H.
Published: June 2006

For n ≥ 1, let Xnl,…, Xnn be independent integer‐valued random variables, and define Sn = Xnl+···+Xnn. In a recent paper, we obtained a simple proof for the convergence of the distribution of Sn to a Poisson distribution under very general conditions. In this paper, we extend that result to the multidimensional case.
Iceberg paths and collision risks for fixed marine structures
Authors: Whitmore G. A. , Gentleman Jane F.
Published: June 2006

Icebergs pose a serious risk to fixed marine structures in northern waters. In this case study, the analysts were provided with three months of data on iceberg movements, weather, and ocean conditions in the vicinity of an oil‐drilling platform in the South Labrador Sea during the 1980 summer drilling season. The analysts' task was to use the data to construct a probabilistic forecasting model of iceberg motion which could provide a platform operator with an estimate of the collision risk posed to the platform by a nearby iceberg.

En eaux nordiques, les icebergs sont une source constante de danger pour les structures flottantes stationnaires érigées au grand large. Pour tenter de mieux cerner ce danger, des observateurs ont été chargés de relever les mouvements des icebergs ainsi que les conditions climatiques et maritimes prévalent dans les parages ďune plate‐forme de forage du sud de la Mer du Labrador. Le cueillette de données s'est poursuivie pendant trois mois au cours de l'été 1980. Les analystes auxquels ces données ont été confiées avaient pour mission de construire un modèle probabiliste apte à prédire les déplacements des icebergs. Le modèle devait permettre en outre ďévaluer les risques de collision auxquels la plate‐forme de forage est exposéc.
One‐sided comparisons for treatments with a control
Authors: Robertson Tim , Wright F. T.
Published: June 2006

Distribution theory for likelihood‐ratio statistics for the comparison of several treatments with a control is discussed. These test statistics account for prior information that the treatments are at least as effective as the control. It is assumed that the sample sizes on the treatments are (approximately) equal and the sample size on the control is at least as large. Normal means are compared under the assumption of a common variance, either known or unknown. The analogous problems for proportions as well as rank tests are mentioned, and the results of a power study comparing a one‐sided t‐test, the likelihood‐ratio test, and Dunnetťs one‐sided test are presented.

Cet article concerne les distributions de statistiques obtenues à partir du quotient de vraisemblance pour la comparison de plusieurs traitements par rapport à un échantillon témoin. Ces statistiques tiennent compte ďinformation préliminaire à l'effet que les traitements seraient tout au moins aussi efficaces que le placébo témoin. On suppose que les tailles des échantillons correspondant aux traitements sont (approximativement) égales et qu'elles sont inférieures à celle de l'échantillon témoin. L'objectif poursuivi est celui de comparer les moyennes de populations normales sous ccrtaines restrictions ďordre et sous l'hypothèse que les variances des populations (connues ou inconnues) sont égales. Les auteurs se servent des techniques de Monte‐Carlo pour comparer de façon empirique les fonctions de puissance des tests de Student, de Dunnett et du quotient de vraisemblance. Les problèmes analogues concernant la comparaison de rangs ou de proportions sont également mentionnés.
Decomposition of models whose marginal distributions are mixtures
Authors: Small Christopher G.
Published: June 2006

The characterization of components of dependent mixture models is studied. The independent mixture model and outlier model are considered as special cases. Applications to modelling outliers in robustness studies are given. It is shown that under certain asymptotic conditions, the components are characterized by the distribution of the mixture model. In such cases, all parametrizations are identifiable.

Nous considérons dans quelle mesure il est possible ďidentifier les composantes ďun mélange de distributions au moyen ďobservations possiblement dépendantes. A titre ďexemple, on peut bien sǔr songer à la situation classique où les observations sont en fait indépendantes, mais nous voulons aussi envisager ici le cas où le mélange se compose de deux distributions dont l'une est jugée aberrante. Sous certaines conditions limites, nous montrons ďabord comment les composantes ďun mélange peuvent ètre caractérisées si l'on connaǐt la distribution conjointe ďun échantillon provenant de ce mélange. Puis, nous appliquons ce résultat à la construction de modèles de valeurs aberrantes dans le cadre ďétudes de robustesse.
On regularity for statistical models
Authors: Evans M. , Fraser D. A. S. , Monette G.
Published: June 2006

Some recent discussions of the logic involved in statistical inference have focussed on the given (i. e. the statistical model and the data) and the role of the common reduction principles (namely conditionality, likelihood, and sufficiency). The minimum statistical model, a class of probability measures on a measurable space, can yield many different density‐function models with consequent arbitrariness for the definition of the likelihood function and with anomalies in the presence of the reduction principles; instances are cited. Restrictions are given for the minimum model; these lead to a canonical definition for density models and for likelihood functions, and to modified definitions for conditionality and sufficiency to avoid the anomalies.

Ces temps derniers, les débats que soulèvent sans cesse l''inférence statistique et ses assises rationnelles ont eu davantage tendance à porter sur ce que l'on pourrait convenir ďappeler les ostensibles, c'est‐à‐dire les données, le modèle qui les sous‐tend, ainsi que l'influence des principes réducteurs coutumiers, à savoir l'exhaustivité, la conditionalisation et le principe de vraisemblance. Dans cet article, nous allons plus loin pour ne considérer que ce qui constitue le strict minimum ďun modèle statistique: un espace mesurable conjugué à une classe de mesures de probabilite. Comme on peut choisir différentes manières ďexprimer ces mesures de probabilité sous forme de densités, la fonction de vraisemblance souffre fatalement ďun certain arbitraire, ce qui provoque parfois des anomalies lorsque l'on invoque les principes réducteurs cités plus haut. En plus de substantier cet énoncé, nous suggérons ici la manière ďéviter cette embǔche en exigeant de tout modèle statistique qu'il satisfasse certaines conditions additionnelles. Ces conditions conduisent à une définition canonique des fonctions de vraisemblance et des modèles qui font intervenir des fonctions de densité. Pour éviter toute anomalie, les définitions des principes de conditionalisation et ďexhaustivité doivent également ětre modifiées. Les éléments structured requis pour le traitement ďautres modèles seront considéréd ailleurs.
Prediction intervals with a Dirichlet‐process prior distribution
Authors: Campbell Gregory , Hollander Myles
Published: June 2006

Let X1, …,Xn, and Y1, … Yn be consecutive samples from a distribution function F which itself is randomly chosen according to the Ferguson (1973) Dirichlet‐process prior distribution on the space of distribution functions. Typically, prediction intervals employ the observations X1,…, Xn in the first sample in order to predict a specified function of the future sample Y1, …, Yn. Here one‐ and two‐sided prediction intervals for at least q of N future observations are developed for the situation in which, in addition to the previous sample, there is prior information available. The information is specified via the parameter α of the Dirichlet process prior distribution.
Robust weighted Cramér‐von Mises Estimators of location, with minimax variance in ϵ‐contamination neighbourhoods
Authors: Wiens Douglas P.
Published: June 2006

We construct weighted Cramér‐von Mises location estimators which are asymptotically normally distributed throughout an ϵe‐contamination neighbourhood of a given, strongly unimodal distribution function, and which minimize the maximum asymptotic variance in such neighbourhoods. Applications to the estimation of a normal or logistic mean are given.
Some exact results on the sample autocovariances of a seasonal ARIMA model
Authors: Latour Alain , Roy Roch
Published: June 2006

A seasonal random walk is an ARIMA process such that the first difference of order s (s ≥ 1) is a white noise. Given a series of observations from a particular linear transformation of a seasonal random walk, we study the autocovariances c'(k) based on uncentered data and the autocovariances c(k) based on centered data. In both cases, we provide exact, explicit formulae for the mean, variance, and covariance of the sample autocovariances. It is seen that the moments of the c(k)'s are different from those of the c'(k)'s, even asymptotically. Several analytical results presented in the paper were derived by using a symbolic manipulation program.
On the probabilities of the log‐zero‐Poisson distribution
Authors: Willmot Gordon E.
Published: June 2006

An explicit finite‐sum expression for the probability function of the log‐zero‐Poisson distribution is given as well as a simple asymptotic formula.

On donne une expression explicite en somme finie de la fonction de masse de probabilité associée à la loi log‐zéro‐Poisson de měme qu'une formule asymptotique simple.
On an improved Erdő‐Rényi‐type law for increments of partial sums
Authors: Huse Vera R. , Steinebach Josef
Published: June 2006

Let X1, X2,… be an independently and identically distributed sequence with ξX1 = 0, ξ exp (tX1 < ∞ (t ≧ 0) and partial sums Sn = X1 + … + Xn. Consider the maximum increment D1 (N, K) = max0≤n ≤ N ‐ K (Sn + K ‐ Sn)of the sequence (Sn) in (0, N) over a time K = KN, 1 ≦ K ≦ N. Under appropriate conditions on (KN) it is shown that in the case KN/log N → 0, but KN/(log N)1/2 → ∞, there exists a sequence (αN) such that K‐1/2 D1 (N, K) ‐ αN converges to 0 w. p. 1. This result provides a small increment analogue to the improved Erdős‐Rényi‐type laws stated by Csörgő and Steinebach (1981).
Local rates of convergence for consistent estimators of location of translation families
Authors: Weiss Günter M. T.
Published: June 2006

We consider the estimation of a location parameter θ in a one‐sample problem. A measure of the asymptotic performance of an estimator sequence {Tn} = T is given by the exponential rate of convergence to zero of the tail probability,

which for consistent estimator sequences is bounded by a constant, B (θ, ϵ), called the Bahadur bound. We consider two consistent estimators: the maximum‐likelihood estimator (mle) and a consistent estimator based on a likelihood‐ratio statistic, which we call the probability‐ratio estimator (pre). In order to compare the local behaviour of these estimators, we obtain Taylor series expansions in ϵ for B (θ, ϵ) and the exponential rates of the mle and pre. Finally, some numerical work is presented in which we consider a variety of underlying distributions.
Shortest confidence intervals for the ratio of two normal variances
Authors: Levy K.J. , Narula S.C.
Published: June 2006

In this paper the shortest confidence interval for the ratio of two variances is derived when the populations are assumed to be normal. A table, which will help in computing the shortest confidence interval, is also provided.
Inverted dirichlet distribution and multivariate logistic distribution
Authors: Yassaee Hedayat
Published: June 2006

In this paper we derive a k‐variate inverted Dirichlet distribution, D ('v1,v2, ···, vk; vk+1) by a theorem related to k+1 independent random variables having gamma distributions with different parameters v1,v2, ···, vk+1 but with the same scale parameter, say 1. A number of results for a k‐variate inverted Dirichlet distribution are proved and it is shown that one may deduce a k‐dimensional multivariate logistic distribution from a k‐variate inverted Dirichlet distribution.
Some finite‐sample‐size properties of rosenblatt density estimates
Authors: Kraft Charles H. , Lepage Yves , Eeden Constance Van
Published: June 2006

The results of a Monte Carlo study of the sensitivity of Rosenblatt density estimates to the scale factor are presented.
An approximation to the distribution of the sample variance
Authors: Solomon Herbert , Stephens Michael A.
Published: June 2006

A simple three‐moment approximation is introduced for the distribution of the sample variance. Comparisons are given with other approximations discussed by Tan and Wong (1977) and with an approximation developed very recently by Mudholkar and Trivedi (1981).
Sampling properties of estimators of a Weibull distribution of use in the lumber industry
Authors: Johnson Richard A. , Haskell James H.
Published: June 2006

We consider maximum‐likelihood estimators of the three parameters in the Weibull distribution. Motivated by an application regarding the determination of a lower percentile of the strength of dimension lumber, we investigate the sampling properties of these estimators. Consistency is established when the shape parameter is greater than one, including some nonregular cases encountered in fitting lumber data. The joint distribution of the estimators is studied by a Monte Carlo approach. The maximum‐likelihood estimator of the 5th percentile is compared with the sample 5th percentile. For the cases considered it was generally found that with sample size 70 the usual asymptotic normality does not hold.
Graphical rational patterns (GRP) application to canadian geostatistical data
Authors: Yam J.
Published: June 2006

This article deals with the application of a new graphical system, known as Graphical Rational Patterns (GRP), to geostatistical data. The first portion of the paper provides a brief review of the system for readers who are unfamiliar with it. This is followed by a series of annotated illustrations based on recent Canadian data. The paper emphasizes that the GRP system is particularly suitable for producing large numbers of inexpensive drafts or experimental maps by non‐cartographers; as such, the system contributes to geostatistical analysis undertaken by demographers, statisticians and others. An attempt is made to substantiate that the GRP system (i) introduces improved arrays of symbols (e.g., with regard to homogeneity and “rationality”); (ii) provides graphs and maps with improved “readability” and transmittance of general trends; (iii) suggests solutions where conventional methods are inapplicable or ineffective.
Estimation of frequencies of sinusoids in the presence of noise
Authors: Ong B. G. , Campbell L. L.
Published: June 2006

A method is proposed and developed for estimating the frequencies of K sinusoids given the sum of these sinusoids in Gaussian noise. Attention is focused on the properties of these estimators when the observation time is short, the separation between frequencies is small, and the signal‐to‐noise ratio is high. The estimators are shown to be approximately unbiased and approximately normally distributed. The covariance matrix is also calculated. Relatively simple bounds on the variance of the estimators are found.
Locally minimax tests for multiple correlations
Authors: Giri N.
Published: June 2006

Let X be a normally distributed p‐dimensional column vector with mean μ and positive definite covariance matrix σ. and let Xα, α = 1,…, N, be a random sample of size N from this distribution. Partition X as (X1, X(2)', X'(3))', where X1 is one‐dimension, X(2) is p2‐ dimensional, and so 1 + p1 + p2 = p. Let ρ1 and ρ be the multiple correlation coefficients of X1 with X(2) and with (X'(2), X'(3))', respectively. Write ρ2/2 = ρ2 ‐ ρ2/1. We shall cosider the following two problems
On additive and multiplicative damage models and the characterizations of linear and logarithmic exponential families
Authors: Patil G. P. , Ratnaparkhi M. V.
Published: June 2006

Rao (1963) has formulated a damage model which we call an additive damage model. A suitable damage model, which we call a multiplicative damage model, has been considered by Krishnaji (1970) for income‐related problems. In these models, an original observation is subjected to damage, e.g., death or under‐reporting, according to a specified probability law. Within the framework of an additive damage model, with a special form of damage, characterizations of the linear and logarithmic exponential families are formulated using regression properties of the damaged part on the undamaged part. The characterizations of the gamma and Pareto distributions that have been found of some use in the theory of income distributions, are obtained as special cases. Similar results are investigated within the framework of the multiplicative damage model.
Maximum‐likelihood estimates and likelihood‐ratio criteria for multivariate elliptically contoured distributions
Authors: Anderson T. W. , Hsu Huang , Fang Kai‐Tai
Published: June 2006

For a class of multivariate elliptically contoured distributions the maximum‐likelihood estimators of the mean vector and covariance matrix are found under certain conditions. Likelihood‐ratio criteria are obtained for a class of null hypotheses. These have the same form as in the normal case.
A remark on self‐similar processes with stationary increments
Authors: Maejima Makoto
Published: June 2006

The upper bound of the parameter of self‐similar processes with stationary increments is given in terms of the moment condition.
Testing multiple slippages
Authors: Singh Ashok K.
Published: June 2006

A class of invariant Bayes rules is derived for testing homogeneity of k (≥2) different populations against (kt) slippage alternatives that some (unknown) subset of size t of the given populations has parameter larger than the remaining k‐t, where t is a given integer between 1 and k‐1. For a similar problem in nonparametric situations, locally best tests based on ranks are derived.
Convergence results for sequences of quadratic forms
Authors: Wilmesmeier James M. , Wright F. T.
Published: June 2006

Let (XI,)be a sequence of independent random variables, and let Qn= where for each N,(an:,k)is a doubly indexed sequence of weights. The convergence and the rate of convergence of the sequence of quadratic forms {Qn} are studied. These quadratic forms are linear sums of dependent variables; however, their convergence properties are similar to those of linear sums of independent variables provided the variables have finite rth absolute moments with 0 < r 2.while the rate of convergence has not been obtained for r< 2, it is shown to be different from that of linear sums.
On the distribution of the likelihood ratio test of equality of normal populations
Authors: Muirhead Robb J.
Published: June 2006

It has recently been shown by Perlman (1980) that when testing the equality of several normal distributions it is the likelihood ratio test which is unbiased rather than a test based on a modified statistic in common use. This paper gives expansions for the null distribution of the likelihood ratio statistic as well as for the nonnull distribution in a special case.
Obtaining efficient estimates of park use and testing for the structural adequacy of models
Authors: Beaman J. , Cheung H.K. , Knetsch J.
Published: June 2006

This paper provides an examination of the problem of heteroscedasticity as it relates to estimating park use, although the results can also be applied to a wide variety of flow problems involving traffic, people or commodities. The major issue is that estimates of flows obtained using ordinary least squares, OLS, often yield statistically significant results while still giving rise to large differences between observed and predicted flows (residuals).

The paper presents results which show that for the flow estimation problem of concern, more accurate use estimates may be obtained by using generalized least squares, GLS, rather than using OLS. Weights to use in GLS regression are developed taking into account the variance to be expected in origin‐destination flows.

It is shown that deriving the correct weights, estimates of variances, to use in a regression analysis results in an ‘absolute’ test for the structural appropriateness of the regression model. Tests related to the ‘absolute’ adequacy test are introduced and their use to identify specific structural problems with a model is illustrated.
Delayed averages of mixing sequences
Authors: Deo Chandrakant M.
Published: June 2006

We obtain a limit theorem for stationary, mixing sequences of random variables.
Power comparisons of single‐sample winsorized T, trimmed T and student's T
Authors: Yuen Karen K.
Published: June 2006

The objective of this study is to evaluate the performance of Winsorized t which was proposed to be used as one alternative to the student's t statistic when the parent population is non‐normal. The criterion we use is the power of the test. Comparative performance of the Winsorized t, trimmed t, and Studen$tCs t for normal populations and for Studen$tCs t distribution with 8, 4, and 2 degrees of freedom was investigated.
Singular gauss‐markov models
Authors: Scobey P.
Published: June 2006

For the general linear model Y = X$sZ + e in which e has a singular dispersion matrix $sG2A, $sG > 0, where A is n x n and singular, Mitra [2] considers the problem of testing F$sZ, where F is a known q x q matrix and claims that the sum of squares (SS) due to hypothesis is not distributed (as a x2 variate with degrees of freedom (d. f.) equal to the rank of F) independent of the SS due to error, when a generalized inverse of A is chosen as (A + X'X)–. This claim does not hold if a pseudo‐inverse of A is taken to be (A + X'X)+ where A+ denotes the unique Moore‐Penrose inverse (MPI) of A.
Sur l'estimation du risque encouru en reconstruisant une forme aléatoire
Authors: Moore Marc , Legault Maurice
Published: June 2006

Le problème de l'estimation du risque encouru en reconstruisant une forme aléatoire est rappelé. Il est montré que dans le cas d'un modèle particulier important, l'estimation de ce risque se ramène à l'estimation de deux paramètres très liés à ceux apparaissant dans une chaîne de Markov à deux états celle‐ci ayant son intérêt propre. Une étude de l'estimation des paramètres de cette chaîne de Markov est effectuée du point de vue de la théorie de la décision. Les estimateurs obtenus sont adaptés à l'estimation de ceux définissant le risque considéré. Des exemples sont analysés. Il est constaté que même en utilisant une méthode très empirique pour déterminer les paramètres des lois a priori, d'excellents estimateurs du risque sont obtenus.
Tests of hypotheses for reliability functions in two‐parameter exponential models
Authors: Ranganathan J. , Kale B. K.
Published: June 2006

This paper derives a test procedure for testing hypotheses about the reliability function of the two‐parameter exponential model. The exact distribution of the test statistic is obtained and it is shown that the test is UMP invariant. Applications to problems in quality control are also considered.
Structured probability statements
Authors: Plante André
Published: June 2006

Structured probability statements are defined in an additive and reduced structured model. Under weak assumptions, an estimating set in a structured probability statement is a confidence region, but the corresponding structured probability may differ from the confidence coefficient. Elementary examples are given to show that this difference is an advantage when some estimating sets are empty or consist of the whole parameter space. A structured distribution (Plante 1979) is an extension of a probability measure closely related to structured probability statements.
Unbiased estimation of the variance of the Graybill‐Deal estimator of the common mean of several normal populations
Authors: Sinha Bimal Kumar
Published: June 2006

An identity for the chi‐squared distribution is used to derive an unbiased estimator of the variance of the familiar Graybill‐Deal (1959) estimator of the common mean of several normal populations with possibly different unknown variances. This result appears to be new. It is observed that the unbiased estimator is a convergent series whose suitable truncation allows unbiased estimation up to any desired degree of accuracy.
On a theorem of Stein relating Bayesian and classical inferences in group models
Authors: Chang Ted , Villegas Cesareo
Published: June 2006

Let a group G act on the sample space. This paper gives another proof of a theorem of Stein relating a group invariant family of posterior Bayesian probability regions to classical confidence regions when an appropriate prior is used. The example of the central multivariate normal distribution is discussed.
On the maximum‐likelihood estimator for the location parameter of a cauchy distribution
Authors: Bai Z. D. , Fu J. C.
Published: June 2006

In the literature of point estimation, the Cauchy distribution with location parameter is often cited as an example for the failure of maximum‐likelihood method and hence the failure of the likelihood principle in general. Contrary to the above notion, we prove that even in this case the likelihood equation has multiple roots and that the maximum‐likelihood estimator (the global maximum) remains as an asymptotically optimal estimator in the Bahadur sense.
L'application de la télédétection à l'estimation des superficies agricoles
Authors: Germain Marie‐France , Julien Claude
Published: June 2006

One of several indicators of cultivated area produced by Statistics Canada combines, by regression estimation, remotely sensed data with ground data collected from a survey with a complex design. This paper presents the methodology used to collect and process data from each source. Four regression estimators along with their variance estimators are given. Of these, two are poststratified. Results obtained from two applications are compared.
Estimating the average number of loss days for acute conditions from the canada health survey
Authors: Paton David G.
Published: June 2006

In the Canada Health Survey a number of questions were posed to enable the estimation of the total number of days that are lost to acute (short‐term) health problems by Canadians. In this paper we show how, under certain assumptions, these data may also be used to obtain estimates of the number of episodes of loss days and hence of the average length of an episode.
Classement des entreprises par groupes de taille a partir de données administratives
Authors: Proulx Joanne , ŞCHIOPU‐KRATINA Ioana
Published: June 2006

This article describes a model which evaluates and assigns the maximum number of employees associated to every enterprise in Canada. This model allows for periodic reclassification by size of the population of the Survey of Employment, Payrolls and Hours (SEPH) and thus curtails the variations of the monthly estimates of the survey. SEPH is based on a sample drawn from a population which is stratified by province, industry group and size. The size of a population unit is defined by its number of employees. Since the SEPH population is very dynamic, the classification by size quickly becomes outdated. The model was developed using administrative data provided by Revenue Canada. Special treatments (filters) were conceived to prevent the possible over‐estimation of the maximum number of employees associated with each unit. Three consecutive applications of the model show that, for 87% of the observed units, the size code assigned by the model is confirmed by data provided by the respondent.
A two‐way classification of regression estimation strategies in probability sampling
Authors: Särndal Carl‐Erik
Published: June 2006

This paper examines strategies for estimating the mean of a finite population in the following situation: A linear regression model is assumed to describe the population scatter. Various estimators β for the vector of regression parameters β are considered. Several ways of transforming each estimator β into a model‐based estimator for the population mean are considered. Some estimators constructed in this way become sensitive to correctness of the assumed model. The estimators favoured in this paper are the ones in which the observations are weighted to reflect the sampling design, so that asymptotic design unbiasedness is achieved. For these estimators, the randomization distribution gives protection against model breakdown.
Towards a unified definition of maximum likelihood
Authors: Scholz F. W.
Published: June 2006

A unified definition of maximum likelihood (ml) is given. It is based on a pairwise comparison of probability measures near the observed data point. This definition does not suffer from the usual inadequacies of earlier definitions, i.e., it does not depend on the choice of a density version in the dominated case. The definition covers the undominated case as well, i.e., it provides a consistent approach to nonparametric ml problems, which heretofore have been solved on a more less ad hoc basis. It is shown that the new ml definition is a true extension of the classical ml approach, as it is practiced in the dominated case. Hence the classical methodology can simply be subsumed. Parametric and nonparametric examples are discussed.
On rates of convergence to infinitely divisible laws for dependent random variables
Authors: Basu A. K.
Published: June 2006

Large O and small o approximations of the expected value of a class of functions (modified K‐functional and Lipschitz class) of the normalized partial sums of dependent random variables by the expectation of the corresponding functions of infinitely divisible random variables have been established. As a special case, we have obtained rates of convergence to the Stable Limit Laws and to the Weak Laws of Large Numbers. The technique used is the conditional version of the operator method of Trotter and the Taylor expansion.
On the construction of balanced and orthogonal arrays
Authors: Chakravarty R. , Dey A.
Published: June 2006

Two series of three symbol balanced arrays of strength two are constructed. Using special classes of BIB designs, two classes of two symbol orthogonal arrays of strength three are constructed.
Large sample interval estimation for the logarithmic series distribution
Authors: Wani J. K. , Lo H. P.
Published: June 2006

It is assumed that a large random sample of fixed size n is drawn from a logarithmic series distribution with parameter $tH and that it is desired to estimate e by means of two‐sided confidence interval. Using asymptotic results, charts of confidence intervals are prepared for n = 50, 100, 200, 500 and 1,000, and confidence coefficients 0.90 and 0.95.
The interplay of optimality and combinatorics in experimental design
Authors: Kiefer Jack C.
Published: June 2006

The design of statistical experiments, as developed by R. A. Fisher and his followers, often used combinatorial structures that yielded simple calculation of estimates and/or symmetric variances and covariances. Examples are block designs with balance, regression experiments with equally spaced observations, etc. More recently, considerations of optimality (choosing a design that achieves most accurate inference in some sense) have sometimes justified the traditional designs, but have sometimes led to new combinatorial investigations. Illustrations are given.
Discrete approximations to the information integral
Authors: Ghurye S. G. , Johnson B. R.
Published: June 2006

If f and g are probability densities on the line, the integral of f ln(f/g) is the Kullback‐Leibler information of f with respect to g. In practice, the observations are discrete, and hence the actual distributions are discrete approximations to the theoretical continuous distributions. This paper is concerned with estimating loss of information due to discretization of data.
The power function and an approximation for testing variance components in the presence of interaction in two‐way random effects models
Authors: Tan W. Y.
Published: June 2006

In this paper we consider a two‐way layout random‐effects model with interaction proportional to the product of two random components and derive the distributions of the sums of squares and the F‐ratio under the usual normality assumption for the random effects. Approximations to these distributions by finite series Laguerre polynomial expansions are then developed. Some numerical results are given to illustrate the applications of the theory.
Binary designs are not always the best
Authors: Shah K. R. , Das Ashish
Published: June 2006

We give an example of a nonbinary block design which is better than any binary design with respect to the E‐optimality criterion. This shows that the class of binary designs is not essentially complete, at least with respect to E‐optimality.
E‐optimal designs for regression models with quantitative factors— a reasonable choice?
Authors: Dette Holger
Published: June 2006

For regression models with quantitative factors it is illustrated that the E‐optimal design can be extremely inefficient in the sense that it degenerates to a design which takes all observations at only one point. This phenomenon is caused by the different size of the elements in the covariance matrix of the least‐squares estimator for the unknown parameters. For these reasons we propose to replace the E‐criterion by a corresponding standardized version. The advantage of this approach is demonstrated for the polynomial regression on a nonnegative interval, where the classical and standardized E‐optimal designs can be found explicitly. The described phenomena are not restricted to the E‐criterion but appear for nearly all optimality criteria proposed in the literature. Therefore standardization is recommended for optimal experimental design in regression models with quantitative factors. The optimal designs with respect to the new standardized criteria satisfy a similar invariance property as the famous D‐optimal designs, which allows an easy calculation of standardized optimal designs on many linearly transformed design spaces.
Cellular telephones and motor‐vehicle collisions: Some variations on matched‐pairs analysis
Authors: Tibshirani Robert , Redelmeier Donald A.
Published: June 2006

We describe the analysis of some matched‐pair binary data arising from a study designed to investigate whether cellular‐telephone use is associated with motor‐vehicle collisions. Conditional and random effects approaches to the problem are derived and compared. Driving intermittency is a potential confounder whose effect is assessed by strategic choices of the control period and by application of the bootstrap. The marked discrepancy between the conditional and random approaches merits further study.
Minimax estimation of a lower‐bounded scale parameter of a gamma distribution for scale‐invariant squared‐error loss
Authors: Eeden Constance Van
Published: June 2006

Let X have a gamma distribution with known shape parameter θr;aL and unknown scale parameter θ. Suppose it is known that θ ≥ a for some known a > 0. An admissible minimax estimator for scale‐invariant squared‐error loss is presented. This estimator is the pointwise limit of a sequence of Bayes estimators. Further, the class of truncated linear estimators C = {θρ|θρ(x) = max(a, ρ), ρ > 0} is studied. It is shown that each θρ is inadmissible and that exactly one of them is minimax. Finally, it is shown that Katz's [Ann. Math. Statist., 32, 136–142 (1961)] estimator of θ is not minimax for our loss function. Some further properties of and comparisons among these estimators are also presented.
On nonparametric Bayesian inference for the distribution of a random sample
Authors: Gelfand Alan E. , Mukhopadhyay Saurabh
Published: June 2006

The nonparametric Bayesian approach for inference regarding the unknown distribution of a random sample customarily assumes that this distribution is random and arises through Dirichlet‐process mixing. Previous work within this setting has focused on the mean of the posterior distribution of this random distribution, which is the predictive distribution of a future observation given the sample. Our interest here is in learning about other features of this posterior distribution as well as about posteriors associated with functionals of the distribution of the data. We indicate how to do this in the case of linear functionals. An illustration, with a sample from a Gamma distribution, utilizes Dirichlet‐process mixtures of normals to recover this distribution and its features.
Estimation of the need for child care in Canada
Authors: Gentleman Jane F. , Whitmore G.A.
Published: June 2006

Finding adequate child care is a serious problem for many Canadian parents. The purpose of this case study is to estimate the need for child care in Canada, including ihc portion of this need that may be hidden. We utilize the Family History Survey conducted by Statistics Canada (1984) to explore patterns of both met and unmet child‐care needs, based, in the latter case, on varying assumptions about the degree of parents' desire for child care.
Analysis of the relationship between air pollution and asthma
Authors: Corey Paul N. , Lou Wen‐Yi , Broder Irv
Published: June 2006

In recent years, considerable attention has been devoted to methods for analyzing longitudinal data. A review of some of the issues surrounding the use of regression analysis is undertaken as they relate to a study of the health effects of air pollution in a group of asthmatics. Daily diary recordings of hours with asthma symptoms are found to be positively related to the daily mean concentration of total reduced sulphur as well as to the daily intake of nonsteroidal drug medication. This finding is corroborated using three different statistical models.
Nonparametric smoothing in the analysis of air pollution and respiratory illness
Authors: Schwartz Joel
Published: June 2006

While most of epidemiology is observational, rather than experimental, the culture of epidemiology is still derived from agricultural experiments, rather than other observational fields, such as astronomy or economics. The mismatch is made greater as focus has turned to continue risk factors, multifactorial outcomes, and outcomes with large variation unexplainable by available risk factors. The analysis of such data is often viewed as hypothesis testing with statistical control replacing randomization. However, such approaches often test restricted forms of the hypothesis being investigated, such as the hypothesis of a linear association, when there is no prior empirical or theoretical reason to believe that if an association exists, it is linear. In combination with the large nonstochastic sources of error in such observational studies, this suggests the more flexible alternative of exploring the association. Conclusions on the possible causal nature of any discovered association will rest on the coherence and consistency of multiple studies. Nonparametric smoothing in general, and generalized additive models in particular, represent an attractive approach to such problems. This is illustrated using data examining the relationship between particulate air pollution and daily mortality in Birmingham, Alabama; between particulate air pollution, ozone, and SO2 and daily hospital admissions for respiratory illness in Philadelphia; and between ozone and particulate air pollution and coughing episodes in children in six eastern U.S. cities. The results indicate that airborne particles and ozone are associated with adverse health outcomes at very low concentrations, and that there are likely no thresholds for these relationships.
Minimax‐variance L‐ and R‐estimators of location
Authors: Wiens Douglas P.
Published: June 2006

We consider the problem of minimax‐variance, robust estimation of a location parameter, through the use of L‐ and R‐estimators. We derive an easily checked necessary condition for L‐estimation to be minimax, and a related sufficient condition for R‐estimation to be minimax. Those cases in the literature in which L‐estimation is known not to be minimax, and those in which R‐estimation is minimax, are derived as consequences of these conditions. New classes of examples are given in each case. As well, we answer a question of Scholz (1974), who showed essentially that the asymptotic variance of an R‐estimator never exceeds that of an L‐estimator, if both are efficient at the same strongly unimodal distribution. Scholz raised the question of whether or not the assumption of strong unimodality could be dropped. We answer this question in the negative, theoretically and by examples. In the examples, the minimax property fails both for L‐estimation and for R‐estimation, but the variance of the L‐estimator, as the distribution of the observation varies over the given neighbourhood, remains unbounded. That of the R‐estimator is unbounded.
Perturbation analysis for an orthogonal least‐squares estimator
Authors: Chapman G. R.
Published: June 2006

Coordinate measuring machines (CMMs) are used to check the geometric integrity of component parts. The geometric constraints to which a part must conform, as defined e.g., by The American National Standards Institute, assume the use of some type of gauging system when inspecting the part. Statistical issues arise in interpretting CMM data in the inspection of part tolerances. We consider a set of n planar regions on the surface of a part. The unit vector normal to each plane is estimated by orthogonal least squares. The small‐sample density of this estimator (on the unit sphere S2) is determined asymptotically as the variance of the CMM error approaches 0. To a first‐degree approximation, this density is Fisher‐von Mises. Diagnostics are reviewed to test the geometric constraint that the n planar regions are oriented correctly with respect to one another, and to test the flatness of planar regions.
Estimating equations, empirical likelihood and constraints on parameters
Authors: Qin Jing , Lawless Jerry
Published: June 2006

Likelihood and estimating‐equation methods provide the two most common approaches to parametric inference. With the former there are three main ways to deal with interval estimation or hypothesis testing; roughly speaking, these are based on the likelihood function, the score function, and the maximum likelihood estimator. For estimating equations which, unlike likelihood, do not require the specification of a full probability distribution for the data, there are analogous methods based on the pseudoscore (estimating function) and on the estimator obtained from the estimating equations. Boos (1992) has given a lucid review, with emphasis on problems that involve constraints on parameters (Aitchison and Silvey 1958). The purposes of this paper are to incorporate empirical likelihood (Owen 1988) into this setting, to compare it with the other methods, and to present some simulations which indicate the need for small‐sample corrections in some situations.

Les méthodes de vraisemblance et des équations d'estimation sont les deux approches à l'inférence paramétrique les plus répandues. Avec la première méthode, il y a trois principales façons de traiter des estimations par intervalle ou des test d'hypothèses; en gros, ces méthodes sont fondées sur la fonction de vraisemblance, la fonction score, et l'estimateur du maximum de vraisemblance. Avec la méthode des équations d'estimation qui, contrairement à la méthode de vraisemblance, ne nécessite pas la spécification d'une loi de distribution complète pour les données, il y existe des méthodes analogues fondées sur le pseudo score (fonction d'estimation) et sur l'estimateur obtenu des équations d'estimation. Boos (1992) a fait une critique lucide, soulignant les problèmes qui impliquent des contraintes sur les paramètres (Aitchison et Silvey 1958). L'objet de cet article est d'introduire la vraisemblance empirique (Owen 1988) dans ce cadre, de la comparer avec les autres méthodes et de présenter quelques simulations qui révèlent la nécessité de corrections de petits échantillons, dans certaines situations.
Asymptotics for multisample statistics
Authors: Vaillancourt Jean
Published: June 2006

Consider a family of square‐integrable Rd‐valued statistics Sk = Sk(X1,k1; X2,k2;…; Xm,km), where the independent samples Xi,kj respectively have ki i.i.d. components valued in some separable metric space Xi. We prove a strong law of large numbers, a central limit theorem and a law of the iterated logarithm for the sequence {Sk}, including both the situations where the sample sizes tend to infinity while m is fixed and those where the sample sizes remain small while m tends to infinity. We also obtain two almost sure convergence results in both these contexts, under the additional assumption that Sk is symmetric in the coordinates of each sample Xi,kj. Some extensions to row‐exchangeable and conditionally independent observations are provided. Applications to an estimator of the dimension of a data set and to the Henze‐Schilling test statistic for equality of two densities are also presented.
Une condition nécessaire d'admissibilité et ses conséquences sur les estimateurs à rétrécisseur de la moyenne d'un vecteur normal
Authors: Fraisse Anne‐Marie , Raoult Jean‐Pierre , Robert Christian , Roy Madeleine
Published: June 2006

Considering exponential families of distributions, we estimate parameters which are not the natural parameters. We prove that the admissible estimators of these parameters are limits of Bayes estimators and can be expressed through a given functional form. An important particular case of this model pertains to the estimation of the mean of a multidimensional normal distribution when the variance is known up to a multiplicative factor. We deduce from the main result a necessry condition for the admissibility of matricial shrinkage estimators.