bluuebunny/crossref_metadata_2025_split huggingface dataset:
Structured probability statements
Authors: Plante André 
Published: June 2006

AbstractStructured 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

AbstractAn 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

AbstractLet 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

AbstractIn 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

AbstractOne 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

AbstractIn 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

AbstractThis 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

AbstractThis 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

AbstractA 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

AbstractLarge 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.
Large sample interval estimation for the logarithmic series distribution
Authors: Wani J. K. , Lo H. P. 
Published: June 2006

AbstractIt 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

AbstractThe 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

AbstractIf 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

AbstractIn 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.
E‐optimal designs for regression models with quantitative factors— a reasonable choice?
Authors: Dette Holger 
Published: June 2006

AbstractFor 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

AbstractWe 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

AbstractLet 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

AbstractThe 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

AbstractFinding 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

AbstractIn 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

AbstractWhile 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

AbstractWe 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

AbstractCoordinate 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

AbstractLikelihood 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

AbstractConsider 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

AbstractConsidering 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.
A winning strategy for lotto games?
Authors: Joe Harry 
Published: June 2006

AbstractIn lotto games, the distribution of k‐tuples chosen by participants is not uniform, but the chance of any k‐tuple being the winner is the same. The winning categories consist of matching exactly k — i numbers from the winning k‐tuple for i = 0, 1, …, m for some m. The total prize pool for a category is divided equally among all the winning tickets in the category. Therefore the strategy of buying a ticket with a k‐tuple consisting of unpopular numbers will increase the expected amount of the prize if this k‐tuple is a winner in some category, because the prize pool is shared among fewer tickets. By modelling the distribution of 6‐tuples chosen by participants of Lotto 6/49 in Canada, the expected return and standard deviation of return can be computed. It is shown that the expected return can be more than the amount spent when the carryover is large, but the large standard deviation means that it would take tens of thousands of years to millions of years for the strategy to have a high probability of yielding a profit.
Asymptotic calculations of functions of expected values and covariances of order statistics
Authors: Stephens M. A. 
Published: June 2006

AbstractSuppose m and V are respectively the vector of expected values and the covariance matrix of the order statistics of a sample of size n from a continuous distribution F. A method is presented to calculate asymptotic values of functions of m and V–1, for distributions F which are sufficiently regular. Values are given for the normal, logistic, and extreme‐value distributions; also, for completeness, for the uniform and exponential distributions, although for these other methods must be used.