bluuebunny/crossref_metadata_2025_split 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

AbstractPlusieurs 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

AbstractWe 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

AbstractFor 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

AbstractIcebergs 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

AbstractDistribution 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

AbstractThe 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

AbstractSome 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

AbstractLet 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

AbstractWe 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

AbstractA 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

AbstractAn 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

AbstractLet 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

AbstractWe 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.
Inverted dirichlet distribution and multivariate logistic distribution
Authors: Yassaee Hedayat 
Published: June 2006

AbstractIn 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.
Sampling properties of estimators of a Weibull distribution of use in the lumber industry
Authors: Johnson Richard A. , Haskell James H. 
Published: June 2006

AbstractWe 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

AbstractThis 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

AbstractA 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

AbstractLet 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

AbstractRao (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

AbstractFor 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.
Testing multiple slippages
Authors: Singh Ashok K. 
Published: June 2006

AbstractA 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

AbstractLet (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

AbstractIt 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

AbstractThis 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.
Power comparisons of single‐sample winsorized T, trimmed T and student's T
Authors: Yuen Karen K. 
Published: June 2006

AbstractThe 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

AbstractFor 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

AbstractLe 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.