bluuebunny/crossref_metadata_2025 huggingface dataset:
A comparison of equally spaced designs with different correlation structures in one and more dimensions
Authors: Herzberg Agnes M. , Huda S.
Published: June 2006

Equally spaced designs are compared using the generalized variance as a measure of efficiency. Results for polynomial models are derived on the increased efficiency arising from increasing the number of design points when the regions are fixed and when the regions are expanded. The effects of dependence among the observations on these results are studied by considering a particular family of stationary correlated error structures.
Distributions of order statistics and estimation of mean life when an outlier may be present
Authors: Sinha S. K.
Published: June 2006

Consider a random sample (X1, X2,…, Xn) where one observation (or out‐lier) is determined by the density f(x, θ/α), θ >0, 0 < α ≤ l, while the remaining observations have a common density f(x, θ) = (l/θ)exp(‐x/θ), with θ > 0. The statistic Tmn = 1/m+1 [Σmi=1 x(i)+(n‐m)x(m)], 0 <m ≤n, was proposed by Kale and Sinha [1] as an estimator of θ treating α as a nuisance parameter. When α= 1, we refer to the above model as homogeneous. In this paper we derive the variance of X(k) the distribution and covariance of (X(k), X(j)), k<j, and show that while the mean‐square error mse(tnn|α→∞, as α→0. the mean‐square error MSE(Tmn|α) remains bounded as α→0.
Categorical information and the singular linear model
Authors: Feuerverger A. , Fraser D. A. S.
Published: June 2006

C. R. Rao (1978) discusses estimation for the common linear model in the case that the variance matrix σ2Q has known singular form Q. In the more general context of inference, this model exhibits certain special features and illustrates how information concerning unknowns can separate into a categorical component and a statistical component. The categorical component establishes that certain parameters are known in value and thus are not part of the statistical inference.
Stochastic game models of brand switching
Authors: Laughland A.R. , Nair K.P.K.
Published: June 2006

In the study of the dynamic nature of brand switching, Markov chain theory has been used extensively. The conflicting interests of the companies involved have, however, not been explicitly incorporated. In this paper, two competing companies, each engaged in marketing a brand product, are considered. Brand switching by a consumer is influenced jointly but probabilistically by the two companies through their respective promotional actions and by the consumer's immediately preceding purchase. A stochastic game model is developed for determining the optimal promotional strategies of the companies, and the unique minimax value of the game in terms of market share. The structure of the model developed is that of a two‐person, zero‐sum, two‐state stochastic game. A method of solution and a few useful variations of the model are présentés. Practical interpretations of the solution are also included.
The distributions of sufficient statistics of truncated generalized logarithmic series, poisson and negative binomial distributions
Authors: Charalambides Ch.A.
Published: June 2006

In this paper the distribution of Z = Σni=1Xi and the joint distribution of Y = min{X1,…,Xn} and Z are obtained in the cases in which X1,…,Xn is a random sample (i) from the left‐truncated generalized logarithmic series distribution in terms of the Stirling numbers of the first kind, (ii) from the left‐truncated generalized Poisson distribution in terms of the Stirling numbers of the second kind and (iii) from the left‐truncated generalized negative binomial in terms of linear combinations of the Stirling numbers of both kinds. These distributions are utilized in order to obtain the minimum variance unbiased estimators of θm, m ≫ 1 when the truncation point r is assumed to be known and of rm and θm when r is unknown.
Exponential models, brownian motion, and independence
Authors: Seshadri V.
Published: June 2006

Some examples of steep, reproductive exponential models are considered. These models are shown to possess a τ‐parallel foliation in the terminology of Barndorff‐Nielsen and Blaesild. The independence of certain functions follows directly from the foliation. Suppose X(t) is a Wiener process with drift where X(t) = W(t) + ct, 0 < t < T. Furthermore let Y = max [X(s), 0 < s < T]. The joint density of Y and X = X(T), the end value, is studied within the framework of an exponential model, and it is shown that Y(Y – X) is independent of X. It is further shown that Y(Y – X) suitably scaled has an exponential distribution. Further examples are considered by randomizing on T.
Improved set estimators for the coefficients of a linear model when the error distribution is spherically symmetric with unknown variances
Authors: Chen Jeesen , Hwang Jiunn T.
Published: June 2006

The usual confidence set for p (p ≥ 3) coefficients of a linear model is known to be dominated by the James‐Stein confidence sets under the assumption of spherical symmetric errors with known variance (Hwang and Chen 1986). For the same confidence‐set problem but for the unknown‐variance case, naturally one replaces the unknown variance by an estimator. For the normal case, many previous studies have shown numerically that the resultant James‐Stein confidence sets dominate the resultant usual confidence sets, i.e., the F confidence sets. In this paper we provide a further asymptotic justification, and we discover the same advantage of the James‐Stein confidence sets for normal error as well as spherically symmetric error.
Recursive improvement of estimates in a Gauss‐Markov model with linear restrictions
Authors: Kala Radoslaw , Kłaczyński Krzysztof
Published: June 2006

The minimum‐dispersion linear unbiased estimator of a set of estimable functions in a general Gauss‐Markov model with double linear restrictions is considered. The attention is focused on developing a recursive formula in which an initial estimator, obtained from the unrestricted model, is corrected with respect to the restrictions successively incorporated into the model. The established formula generalizes known results developed for the simple Gauss‐Markov model.
Estimation in an empirical bayes model for longitudinal and cross‐sectionally clustered binary data
Authors: Sashegyi Andreas I. , Brown K. Stephen , Farrell Patrick J.
Published: June 2006

Some studies generate data that can be grouped into clusters in more than one way. Consider for instance a smoking prevention study in which responses on smoking status are collected over several years in a cohort of students from a number of different schools. This yields longitudinal data, also cross‐sectionaliy clustered in schools. The authors present a model for analyzing binary data of this type, combining generalized estimating equations and estimation of random effects to address the longitudinal and cross‐sectional dependence, respectively. The estimation procedure for this model is discussed, as are the results of a simulation study used to investigate the properties of its estimates. An illustration using data from a smoking prevention trial is given.
Comparing confidence intervals for the logarithmic series distribution
Authors: Wani J. K. , Lo H. P.
Published: June 2006

It is assumed that a small random sample of fixed size n is drawn from a logarithmic series distribution with parameter θ and that it is desired to estimate θ by means of a two‐sided confidence interval. In this note Crow's system of confidence intervals is compared, in shortness of intervals, with Clopper and Pearson's, and the corresponding randomized counterparts.
Asymptotic results for empirical and partial‐sum processes: A review
Authors: Pyke Ronald
Published: June 2006

Two processes of importance in statistics and probability are the empirical and partial‐sum processes. Based on d‐dimensional data X1, … Xa the empirical measure is defined for any A ⊂ Rd by

the sample proportion of observations in A. When normalized, Fn yields the empirical process Wn: = n1/2 (Fn ‐ F), where F denotes the “true” probability measure.

To define partial‐sum processes, one needs data that are assigned to specified locations (in contrast to the above, where specified unit masses are assigned to random locations). A suitable context for many applications is that of data attached to points of a lattice, say {Xj:j ϵ Jd} where J = {1, 2,…}, for which the partial sums are defined for any A ⊂ Rd by

Thus S(A) is the sum of the data contained in A. When normalized, S yields the partial‐sum process. This paper provides an overview of asymptotic results for empirical and partial‐sum processes, including strong laws and central limit theorems, together with some indications of their inferential implications.
Least squares theory for possibly singular models
Authors: Rao C. Radhakrishna
Published: June 2006

In a recent paper, Scobey (1975) observed that the usual least squares theory can be applied even when the covariance matrix σ2V of Y in the linear model Y = Xβ + e is singular by choosing the Moore‐Penrose inverse (V+XX′)+ instead of V‐1 when V is nonsingular. This result appears to be wrong. The appropriate treatment of the problem in the singular case is described.
Change of origin and scale in ratio and difference methods of estimation in sampling
Authors: Srivenkataramana T.
Published: June 2006

This paper discusses two estimators of the mean of a finite population based on a simple random sample from it, when supplementary information on a variable positively correlated with the variable of interest is available. Simultaneous reductions in absolute bias and mean square error of the estimator are seen as compared with those of the traditional estimator in the ratio method of estimation. The suggested estimators are simple for computation and there is no appreciable increase in the cost as well.
Quota fulfillment times
Authors: Anderson Keaven , Sobel Milton , Uppuluri V. R. R.
Published: June 2006

An example of the classical occupancy problem is to sample with replacement from an urn containing several colours of balls and count the number of balls sampled until a given number of “quotas” are filled. This and the corresponding random variable for sampling without replacement will be referred to as quota fulfillment times. Asymptotic and exact methods for computing moments and distributions are given in this paper. Moments of quota fulfillment times are related to moments of order statistics of beta and gamma random variables. Most of the results for sampling without replacement and some of the results for sampling with replacement are believed to be new. Some other known sampling‐with‐replacement results are given for comparative purposes.
A note on multivariate linear exponential distributions
Authors: Doss D.C.
Published: June 2006

A distribution admitting the moment generating function (mgf) is a member of one and only one linear exponential family Pμ = {Pω:ω ϵ Ωμ} with dPω(x) = {eω'x/f(ω)} dμ(x). Factorization of the mgf of a member of a linear exponential family into a finite number of mgf's of linear exponential distributions, implies such a factorization for all members of the family. Consequently, infinite divisibility of the mgf of a member of a linear exponential family implies infinite divisibility for all members of the family.
A characterization of the general mean
Authors: Weerahandi Samaradasa , Zidek James V.
Published: June 2006

A characterization is given of the general mean which is (∂Xp)1/p or exp[log X] for X > 0 according as ρ ≠0 or ρ = 0, where ρ is an unspecified parameter. The approach is axiomatic. The general mean is defined as any quantity satisfying certain axioms which embrace the minimal requirements that any reasonable candidate for the role of mean or most typical value should satisfy. The quantity, indexed by p and given above, is uniquely implied by these axioms.
Comparison of efficient L‐ and R‐estimators of location
Authors: Froda Sorana
Published: June 2006

Scholz (1974) proved that the asymptotic variance of an R‐estimator of location is no larger than that of an L‐estimator when the observations come from a distribution G different from the distribution F for which the two estimators are efficient. This note extends this result to distributions F whose density has a first but no second derivative.
Effect of correlation on the estimation of a mean in the presence of spurious observations
Authors: Guttman Irwin , Tiao G. C.
Published: June 2006

This paper examines the effect of correlation of observations on estimators of a mean which are designed to guard against the possibility of spurious observations (that is, observations generated in a manner not intended). The mean squared error, premium and protection of these estimators are evaluated and discussed for some specific correlation structures.
Statistical issues in epidemiologic studies of the health effects of ambient acid aerosols
Authors: Ware James H. , Stram Daniel O.
Published: June 2006

Although the ecologic effects of acid rain have been widely reported, relatively little is known about the effects of acidic air pollution on human health. Some epidemiologic and animal studies suggest, however, that acidity is an important determinant of the respiratory health effects of aerosols. This paper reviews some of that evidence and discusses its implications for the design and analysis of epidemiologic studies. We contrast two types of exposure patterns: peak exposures associated with air pollution episodes, and chronic exposures resulting from persistently high levels of air pollutants. Recent work on the analysis of repeated categorical outcome variables provides new methods for the analysis of episode studies. Studies of long‐term exposure require comparisons among population groups, and these comparisons can be subject to the design effects characteristic of multistage sample surveys. We examine the implications of these design effects for epidemiologic studies. Finally, the paper discusses the measurement errors induced by the use of outdoor measurements to quantify personal exposure to air pollutants. Recent work on methods for errors‐in‐variables problems may aid in assessing the effects of such errors on conventional analyses of air‐pollution studies.
Criteria for the equality between ordinary least squares and best linear unbiased estimators under certain linear models
Authors: Baksalary Jerzy K.
Published: June 2006

A new necessary and sufficient condition is derived for the equality between the ordinary least‐squares estimator and the best linear unbiased estimator of the expectation vector in linear models with certain specific design matrices. This condition is then applied to special cases involving one‐way and two‐way classification models.
Lightning detection in British Columbia: An example of using system operation at unknown reliability to estimate component reliability
Authors: Johnson Bruce R.
Published: June 2006

Lightning data collected over three dry seasons from the detection system operated by the British Columbia Ministry of Forests were analyzed to estimate the distribution of lightning signal strength and component detection efficiencies. The analysis was based on more than 165,000 lightning‐strike records, where component detectors served both as lightning finders and as data collectors for evaluating the performance of other component detectors in the network. In spite of the unusual feature of this application involving a system evaluating itself, much was revealed to identify weaknesses and suggest improvements. A postanalysis system‐modification update is included.
Jackknifing L‐estimates
Authors: Cheng Kuang‐Fu
Published: June 2006

Linear functions of order statistics (“L‐estimates”) of the form Tn =under jackknifing are investigated. This paper proves that with suitable conditions on the function J, the jackknifed version Tn of the L‐estimate Tn has the same limit distribution as Tn. It is also shown that the jackknife estimate of the asymptotic variance of n1/2 is consistent. Furthermore, the Berry‐Esséen rate associated with asymptotic normality, and a law of the iterated logarithm of a class of jackknife L‐estimates, are characterized.
THE non‐null distribution of the likelihood ratio criterion for testing the hypothesis that the covariance matrix is diagonal
Authors: Mathai A.M. , Tan W.Y.
Published: June 2006

This article deals with the exact non‐null distribution of the likelihood ratio criterion for testing the hypothesis that the covariance matrix in a multinormal distribution is diagonal. The exact non‐null moments as well as the exact non‐null distribution are derived. The distribution is also expressed in computable form with the help of inverse Mellin transform and calculus of residues. The results obtained in this article are useful in studying the power of testing several correlation coefficients simultaneously.
A distribution‐free approach to qdantal response assays
Authors: Shuster Jonathan J. , Yang Mark C. K.
Published: June 2006

A nonparametric method is developed to estimate the minimum dosage level required to induce a given response rate in an experiment. The only assumption used about the response rate is that it is a nondecreasing function with respect to the dosage level. Let nisubjects be independently tested at dosage level xix1x2xk. This paper presents methodology for the estimation of the smallest i such that the response probability at xi is no less than a required level p. A comparison with well‐known nonparametric methods shows that this method is better in some cases. A design of minimum required sample size for a given accuracy is also developed.
LOI conditionnelle de la statistique d'ordre 1 $dcun echantillon: Application
Authors: Colin Bernard
Published: June 2006

A propos $dCun algorithme utilis$eA en recherche op$eArationnelle, nous tenterons $dC$eAtablir une d$eApendance, entre la somme de n observations ind$eApendantes d'une variable al$eAatoire et le minimum de ces observations.
Models and methods for pairing data
Authors: Jong Piet De , Greig Malcolm
Published: June 2006

This paper deals with models and methods for count data derived from observations on pairing phenomena. Pairs formed from “similar” members are excluded. Various models are considered and analyzed. Particular emphasis is on developing methods for testing whether particular pairs are prone to occur more or less often than expected by chance.
Martingale generalizations and preservation of martingale properties
Authors: James Tomkins R.
Published: June 2006

This article investigates circumstances under which seven important martingale properties are preserved by the following six martingale generalizations: quasimartingales, amarts, martingales in the limit, games fairer with time, progressive martingales, and eventual martingales.
Bootstrap and other methods to measure errors in survey estimates
Authors: Kovar J. G. , Rao J. N. K. , Wu C. F. J.
Published: June 2006

Variance estimation techniques for nonlinear statistics, such as ratios and regression and correlation coefficients, and functionals, such as quantiles, are reviewed in the context of sampling from stratified populations. In particular, resampling methods such as the bootstrap, the jackknife, and balanced repeated replication are compared with the traditional linearization method for nonlinear statistics and a method based on Woodruff's confidence intervals for the quantiles. Results of empirical studies are presented on the bias and stability of these variance estimators and on confidence‐interval coverage probabilities and lengths.
Estimating the variance of raking‐ratio estimators
Authors: Binder D. A. , Théberge A.
Published: June 2006

This paper is concerned with the asymptotic properties of the converged solution of the raking‐ratio estimator. After a description of the raking‐ratio estimation procedure, we show that the estimator can be unbiased in the presence of nonresponse if the nonresponse has a particular structure. We also give the asymptotic variance of the estimator. Finally, the results of two numerical applications are presented.
Application des séries chronologiques à l'étude des révisions
Authors: Lefrançois Bernard
Published: June 2006

Time series analysis is applied to the revisions made to a subset of the Canadian National Accounts, in order to determine if, and how, the preliminary figures currently released can be improved toward the first annually figures. Better estimates of period‐to‐period change could thus be obtained. The main findings are that the preliminary figures could be improved, and that this would follow from a modification to the benchmarking methods.

An English version of this paper is available upon request.
Use of questions on activities of daily living to screen for disabled persons in a household survey
Authors: Binder David A. , Morin Jean‐Pierre
Published: June 2006

In recent years, there has been increasing interest in conducting surveys to establish baseline data on the needs and characteristics of the disabled. To respond to this demand, Statistics Canada launched a program in 1982 to survey this population. Several surveys have since been conducted, using as a screening criterion for potentially disabled persons an adaptation of the Activities of Daily Living (ADLs), first developed by the Organization for Economic Co‐operation and Development (OECD). Other health‐related surveys have also been conducted which have incorporated these same ADLs, but not for the express purpose of conducting a survey of the disabled. Whereas these separate surveys had many commonalities, there were certain important differences, which led to remarkably different screening rates. In this paper we study in detail the nature of these differences. We suggest a number of factors which can seriously affect the rates of screening, one of which is the mode of data collection, especially with respect to whether the survey contains additional components which are directed at obtaining information on the disabled.
Partial differential equations for hypergeometric functions 3F2 of matrix argument
Authors: Fujikoshi Yasunori
Published: June 2006

Many multivariate non‐null distributions and moment formulas can be expressed in terms of hypergeometric functions pFq of matrix arqument. Muirhead [6] and Constantine and Muirhead [2] gave partial differential equations for the functions of 2F1 of one argument matrix and two argument matrices, respectively. Such differential equations have been used to obtain asymptotic expansions of the functions (Muirhead [7], [8], [9], Sugiura [10]). The purpose of this paper is to derive partial differential equations for the functions 3F2 (a1 a2, a3; b1, b2, R) and 3F2 (a1, a2, a3; b1, b2; R, S). Differential equations for 2F2 are also obtained.
Bayesian estimates of predictive value and related parameters of a diagnostic test
Authors: Viana Ma G. , Ramakrishnan V.
Published: June 2006

Bayesian analysis of predictive values and related parameters of a diagnostic test are derived. In one case, the estimates are conditional on values of the prevalence of the disease; in the second case, the corresponding unconditional estimates are presented. Small‐sample point estimates, posterior moments, and credibility intervals for all related parameters are obtained. Numerical methods of solution are also discussed.
Strong invariance principles for triangular arrays of weakly dependent random variables
Authors: Dabrowski Andre Robert , Zoglat Abdelhak
Published: June 2006

We establish a strong invariance principle for triangular arrays of a broad class of weakly dependent real random variables. We approximate the original array of dependent random variables by an array of rowwise independent standard normal variables. We demonstrate the functional central limit theorem and law of the iterated logarithm for the approximating array and thereby extend these results to the original array. Among several examples, we look at arrays used in describing the rate of convergence of estimators in regression analysis.
Estimating powers of the generalized variance under the Pitman closeness criterion
Authors: Kubokawa Tatsuya
Published: June 2006

For estimating powers of the generalized variance under a multivariate normal distribution with an unknown mean, the inadmissibility of the closest affine equivariant estimator is shown for the Pitman closeness criterion.
Modifications of the Mack‐Wolfe umbrella tests for a generalized Behrens‐Fisher problem
Authors: Chen Y. I. , Wolfe D. A.
Published: June 2006

We are concerned with testing procedures for umbrella alternatives in the k‐sample location problem without making the assumption that the underlying populations have the same shape. Modifications of the Mack‐Wolfe tests are proposed for the cases when the peak of the umbrella is known or unknown. The proposed procedures are exactly distribution‐free when the continuous populations have the same shape. The modified test for peak‐known umbrella alternatives remains asymptotically distribution‐free when the continuous populations are symmetric, but not necessarily with the same shape.
A complete solution to the problem of robustness of Grubbs's test
Authors: Baksalary Jerzy K. , Puntanen Simo
Published: June 2006

Srivastava (1980) showed that Grubbs's test for detecting a univariate outlier is robust against the effect of intraclass correlation structure. Young, Pavur, and Marco (1989) extended this result by proving that both the significance level and the power of Grubbs's test remain unchanged within a wider family of dispersion matrices, introduced by Baldessari (1966) in a different context. In this note, we derive a complete solution of the problem by establishing that the characteristics of Grubbs's test are invariant with respect to a given dispersion matrix if and only if it has Baldessari's structure.
On prediction and mean squared error
Authors: Yatracos Yannis G.
Published: June 2006

Practical questions motivate the search for predictors either of an as yet unobserved random vector, or of a random function of a parameter. An extension of the classical UMVUE theory is presented to cover such situations. In includes a Rao‐Blackwell‐type theorem, a Cramer‐Rao‐type inequality, and necessary and sufficient conditions for a predictor to minimize the mean squared error uniformly in the parameter. Applications are considered to the problem of selected means, the species problem, and the examination of some u‐v estimates of Robbins (1988).
Inequalities for the partial sums of elliptical order statistics related to genetic selection
Authors: Fang Kai‐Tai , Liang Jia‐Juang
Published: June 2006

Let X1,…,Xn be exchangeable normal variables with a common correlation p, and let X(1) > … > X(n) denote their order statistics. The random variable σni=n—k+1xi, called the selection differential by geneticists, is of particular interest in genetic selection and related areas. In this paper we give results concerning a conjecture of Tong (1982) on the distribution of this random variable as a function of ρ. The same technique used can be applied to yield more general results for linear combinations of order statistics from elliptical distributions.
Asymptotic optimality of a class of rank tests for replicated latin‐square designs
Authors: Monga E. , Tardif S.
Published: June 2006

This paper is concerned with the class of conditionally distribution‐free rank tests introduced by Monga and Tardif (1994) for replicated Latin‐square designs. It is possible to proceed with an enlargement of this class by making use of the method of ranking after substitution. The unconditional asymptotic behaviour of any member of the enlarged class is derived under the null hypothesis of no treatment effects as well as under a sequence of contiguous alternatives. This enables the establishment of the asymptotic Pitman efficiency of any member relative to the asymptotically minimax test and to conclude that at least one member of the class is asymptotically as efficient as the latter.
Convergence rates of change‐point estimators and tail probabilities of the first‐passage‐time process
Authors: Baron Michael
Published: June 2006

In the classical setting of the change‐point problem, the maximum‐likelihood estimator and the traditional confidence region for the change‐point parameter are considered. It is shown that the probability of the correct decision, the coverage probability and the expected size of the confidence set converge exponentially fast as the sample size increases to infinity. For this purpose, the tail probabilities of the first passage times are studied. General inequalities are established, and exact asymptotics are obtained for the case of Bernoulli distributions. A closed asymptotic form for the expected size of the confidence set is derived for this case via the conditional distribution of the first passage times.
Limit theory for autoregressive‐parameter estimates in an infinite‐variance random walk
Authors: Knight Keith
Published: June 2006

We consider the asymptotic behaviour of least‐squares and M‐estimates of the autoregressive parameter when the process is an infinite‐variance random walk. It is shown that certain M ‐estimates converge faster than least‐squares estimates and that they are also asymptotically normal.
On the relation between Hodges‐Lehmann efficiency and Pitman efficiency
Authors: Kourouklis Stavros
Published: June 2006

The relation between Hodges–Lehmann efficiency and Pitman efficiency is studied in the context of testing one‐sided hypotheses about a real‐valued parameter. It is first shown that for tests based on sums of independently and identically distributed observations local Hodges‐Lehmann efficiency is equivalent to Pitman efficiency. Then, it is proved that this equivalence also carries over to tests based on two broad classes of M ‐estimators for the location problem. In all cases considered explicit formulas of the Hodges‐Lehmann efficacies are obtained.
First‐passage densities of controlled Gaussian processes
Authors: Lefebvre Mario
Published: June 2006

Whittle has proved a theorem that gives the optimal control of Gaussian processes in terms of the mathematical expectation of a function of the time and the place where the uncontrolled processes hit the boundary of the stopping region for the first time. In this paper we obtain formulae for the joint probability density function of the first hitting time and place and, in the time‐invariant case, for the moment generating function of the first exit time of the optimally controlled processes. Two particular one‐dimensional cases are considered.
Bounded‐influence rank estimation in the linear model
Authors: Wiens Douglas , Zhou Julie
Published: June 2006

We introduce and study a class of rank‐based estimators for the linear model. The estimate may be roughly described as being calculated in the same manner as a generalized M‐estimate, but with the residual being replaced by a function of its signed rank. The influence function can thus be bounded, both as a function of the residual and as a function of the carriers. Subject to such a bound, the efficiency at a particular model distribution can be optimized by appropriate choices of rank scores and carrier weights. Such choices are given, with respect to a variety of optimality criteria. We compare our estimates with several others, in a Monte Carlo study and on a real data set from the literature.
Asymptotic distributions of functions of a sample covariance matrix under the elliptical distribution
Authors: Iwashita Toshiya , Siotani Minoru
Published: June 2006

This paper is concerned with asymptotic distributions of functions of a sample covariance matrix under the elliptical model. Simple but useful formulae for calculating asymptotic variances and covariances of the functions are derived. Also, an asymptotic expansion formula for the expectation of a function of a sample covariance matrix is derived; it is given up to the second‐order term with respect to the inverse of the sample size. Two examples are given: one of calculating the asymptotic variances and covariances of the stepdown multiple correlation coefficients, and the other of obtaining the asymptotic expansion formula for the moments of sample generalized variance.
Efficiency of reduced logistic regression models
Authors: Bull Shelley B. , Greenwood Celia M.T. , Donner Allan
Published: June 2006

One feature of the usual polychotomous logistic regression model for categorical outcomes is that a covariate must be included in all the regression equations. If a covariate is not important in all of them, the procedure will estimate unnecessary parameters. More flexible approaches allow different subsets of covariates in different regressions. One alternative uses individualized regressions which express the polychotomous model as a series of dichotomous models. Another uses a model in which a reduced set of parameters is simultaneously estimated for all the regressions. Large‐sample efficiencies of these procedures were compared in a variety of circumstances in which there was a common baseline category for the outcome and the covariates were normally distributed. For a correctly specified model, the reduced estimates were over 100% efficient for nonzero slope parameters and up to 500% efficient when the baseline frequency and the effect of interest were small. The individualized estimates could have efficiencies less than 50% when the effect of interest was large, but were also up to 130% efficient when the baseline frequency was large and the effect of interest was small. Efficiency was usually enhanced by correlation among the covariates. For an underspecified reduced model, asymptotic bias in the reduced estimates was approximately proportional to the magnitude of the omitted parameter and to the reciprocal of the baseline frequency.
An optimal experimental design for the haar regression model
Authors: Herzberg Agnes M. , TRAVES William N.
Published: June 2006

The D‐optimal design for the Haar wavelet system is obtained and an example given.
On‐line control procedures under the random‐walk model with measurement error and attribute observations
Authors: Srivastava M.S. , Wu Yanhong
Published: June 2006

Assuming the quality characteristic process follows the random‐walk model, the economic online control procedures are investigated by using the boundary correction technique when (1) the noise or measurement error follows either the random‐walk model or the pure random model, and (2) the observations are taken by attributes only. Simple approximations for the long‐run cost rate and optimal‐control parameters are obtained.
On the Edgeworth expansion and bootstrap approximation for the cox regression model under random censorship
Authors: Gu Minggao
Published: June 2006

We establish the one‐term Edgeworth expansion for various statistics related to Cox semipara‐metric regression model when the covariate is one‐dimensional and the observations are i.i.d. We show that the bootstrap approximation method is second‐order correct. The second‐order‐correct estimates of the sampling distribution can be obtained without Monte Carlo simulation. We pay special attention to the Studentized version of the statistics and show that their distributions are different from those of the original statistics to order n‐½
Monotonic minimax estimators of a 2×2 covariance matrix
Authors: Perron François
Published: June 2006

Let S : 2 × 2 have a nonsingular Wishart distribution with unknown matrix σ and n degrees of freedom. For estimating σ two families of mimmax estimators, with respect to the entropy loss, are presented. These estimators are of the form σ(S) = Rø(L)Rt where R is orthogonal, L and Φ are diagonal, and RLRT = S. Conditions under which the components of Φ and L follow the same order relation [i.e., writing Φ = diag(Φ1,Φ2) and L = diag(l1,/2) with l1 ≥ l2, we have Φ1 ≥ Φ2] are established. Comparisons with Stein's estimators and other orthogonally invariant estimators are discussed.
Prior elicitation in the classification problem
Authors: Cooleyd Craig A. , Maceachern Steven N.
Published: June 2006

Results are developed concerning the asymptotic behaviour of the Bayes classification rule as the number of unclassified observations grows without bound. It is shown that unclassified observations serve only to estimate the individual population parameters in an unlabeled sense and do not provide information about the labels that are attached to the populations. Prior construction is approached through investigation of prior odds over regions of the joint parameter space (across all populations) deemed likely to contain the true joint parameter vector. It is shown that consideration of these prior odds can lead to more robust a posteriori classification of individual observations.
Designs for approximately linear regression: Maximizing the minimum coverage probability of confidence ellipsoids
Authors: Wiens Douglas P.
Published: June 2006

The classical D‐optimality principle in regression design may be motivated by a desire to maximize the coverage probability of a fixed‐volume confidence ellipsoid on the regression parameters. When the fitted model is exactly correct, this amounts to minimizing the determinant of the covariance matrix of the estimators. We consider an analogue of this problem, under the approximately linear model E[y|x] = θTz(x) + f(x). The nonlinear disturbance f(x) is essentially unknown, and the experimenter fits only to the linear part of the response. The resulting bias affects the coverage probability of the confidence ellipsoid on θ. We study the construction of designs which maximize the minimum coverage probability as f varies over a certain class. Explicit designs are given in the case that the fitted response surface is a plane.
On priors that match posterior and frequentist distribution functions
Authors: Ghosh J.K. , Mukerjee Rahul
Published: June 2006

In the multiparameter case, this paper characterizes priors so as to match, up to o(n‐1/2), the posterior joint cumulative distribution function (c.d.f.) of a posterior standardized version of the parametric vector with the corresponding frequentist c.d.f.
Improving on truncated linear estimates of exponential and gamma scale parameters
Authors: Shao Peter Yi‐Shi , Strawderman William E.
Published: June 2006

We consider the problem of estimating the scale parameter of an exponential or a gamma distribution under squared error loss when the scale parameter θ is known to be greater than some fixed value θ0. Natural estimators in this setting include truncated linear functions of the sufficient statistic. Such estimators are typically inadmissible, but explicit improvements seem difficult to find. Some are presented here. A particularly interesting finding is that estimators which are admissible in the untruncated problem which take values only in the interior of the truncated parameter space are found to be inadmissible for the truncated problem.
Jackknife inference for heteroscedastic linear regression models
Authors: Shao Jun , Rao J. N. K.
Published: June 2006

Inference on the regression parameters in a heteroscedastic linear regression model with replication is considered, using either the ordinary least‐squares (OLS) or the weighted least‐squares (WLS) estimator. A delete‐group jackknife method is shown to produce consistent variance estimators irrespective of within‐group correlations, unlike the delete‐one jackknife variance estimators or those based on the customary δ‐method assuming within‐group independence. Finite‐sample properties of the delete‐group variance estimators and associated confidence intervals are also studied through simulation.
Dynamic sampling plans in on‐line control charts
Authors: Wu Yanhong , Srivastava M. S.
Published: June 2006

Three simple dynamic sampling plans for detecting the change point are investigated in the discrete‐time case. The first is a two‐rate sampling CUSUM procedure. The second is a two‐rate sampling Shiryayev‐Roberts procedure. The third is a periodic sequential testing procedure. Two problems are discussed. First, simple design methods are provided for practical use. Second, a comparison between the three plans is made in the continuous‐time case, which shows that by properly choosing the design parameters, the three plans can be made equally efficient in certain senses.
Constrained nonparametric maximum‐likelihood estimation for mixture models
Authors: Susko E. , Kalbfleisch J. D. , Chen J.
Published: June 2006

A nonparametric mixture model specifies that observations arise from a mixture distribution, ∫ f(x, θ) dG(θ), where the mixing distribution G is completely unspecified. A number of algorithms have been developed to obtain unconstrained maximum‐likelihood estimates of G, but none of these algorithms lead to estimates when functional constraints are present. In many cases, there is a natural interest in functional ϕ(G), such as the mean and variance, of the mixing distribution, and profile likelihoods and confidence intervals for ϕ(G) are desired. In this paper we develop a penalized generalization of the ISDM algorithm of Kalbfleisch and Lesperance (1992) that can be used to solve the problem of constrained estimation. We also discuss its use in various different applications. Convergence results and numerical examples are given for the generalized ISDM algorithm, and asymptotic results are developed for the likelihood‐ratio test statistics in the multinomial case.
Applications of a simple regression model to acid rain data
Authors: Stein Michael L. , Shen Xiaotong , Styer Patricia E.
Published: June 2006

This paper addresses two vital and seemingly simple questions concerning wet deposition of sulfates, a major contributor to acid rain. The first is to estimate the annual wet deposition of sulfate at a monitoring site under emissions that existed during the 1980s. This problem is complicated by missing data. The second is to estimate accurately the effect of a change in pollution emissions on concentrations of sulfate in precipitation. This problem is made difficult by the substantial natural variations in sulfate concentrations due to weather variations between years. As a tool for addressing both of these problems, we develop a regression model for the sulfate concentration of precipitation on a particular day as a function of amount of precipitation and time of the year. The model is used as a basis for imputing missing sulfate concentrations to handle the missing‐data problem. It is also used to explain some of the variability in annual sulfate concentrations due to meteorology and hence provide more accurate estimates of the effect of changes in emissions.
Transect‐spacing design of ice cores on the Antarctic continent
Authors: Cressie Noel
Published: June 2006

Chemical analyses of ice cores, drilled deep into an ice sheet, provide a historical record of the earth's atmosphere that dates back as far as 400,000–500,000 years. Although the atmosphere mixes quite well, it is recognized that spatial variability associated with ice‐core locations should be allowed for. In this article, spatial statistical methodology is applied to the design question of finding the best spacing of ice‐core locations on a partial transect of Antarctica.
Efficient estimation in a nonlinear counting‐process regression model
Authors: Greenwood P. E. , Wefelmeyer W.
Published: June 2006

Suppose we observe i.i.d. copies of X, C, Y, where X is a counting process, C is a censoring process talcing only values 0 and 1, and Y is a covariate process. Assume that the intensity process of X is of the form C(s)a(s, Y(s)) with a unknown, but that the distribution of X, C, Y is unspecified otherwise. McKeague and Utikal proposed an estimator for the doubly cumulative hazard f f a(s, y) ds dy and determined its asymptotic distribution. We show that the estimator is regular and efficient in the sense of a Hájek‐Inagaki convolution theorem for partially specified models.
Distributions minimizing fisher information for scale in kolmogorov neighbourhoods
Authors: Wiens Douglas P. , Wu K. H. Eden
Published: June 2006

We construct those distributions minimizing Fisher information for scale in Kolmogorov neighbourhoods Kϵ(G) = {F|supx|F(x) ‐ G(x| ⩽ ϵ} of d.f.'s G satisfying certain mild conditions. The theory is sufficiently general to include those cases in which G is normal, Laplace, logistic, Student's t, etc. As well, we consider G(x) = 1 ‐ e‐x, ⩽ 0, and correct some errors in the literature concerning this case.
Mixture models for matched pairs
Authors: Lesperance Mary L. , Kalbfleisch John D.
Published: June 2006

Mixture models for matched pairs arise when the pair‐specific parameter is assumed to be a random quantity. We explore the use of semiparametric maximum‐likelihood methods for a family of mixture models for matched pairs. The geometry of mixture likelihoods provides insight into the properties of these models.
A modified chi‐square test of independence against a class of ordered alternatives in an r x c contingency table
Authors: Oluyede Broderick O.
Published: June 2006

A modified chi‐square test statistic is constructed for testing the hypothesis of independence in a two‐way contingency table against a class of ordered alternatives defined in terms of pooled cross‐product ratios. The test procedure can also be used to test for positive quadrant dependence in a two‐way contingency table. The asymptotic distribution of the test statistic under the null hypothesis is obtained. Some power comparisons with known test procedures are given. A numerical example is given to illustrate the use of this test.
Practicing safe statistics with the mid‐p
Authors: Routledge R.D.
Published: June 2006

The mid‐p‐value is the standard p‐value for a test minus half the difference between it and the nearest lower possible value. Its smaller size lends it an obvious appeal to users — it provides a more significant‐looking summary of the evidence against the null hypothesis. This paper examines the possibility that the user might overstate the significance of the evidence by using the smaller mid‐p in place of the standard p‐value. Routine use of the mid‐p is shown to control a quantity related to the Type I error rate. This related quantity is appropriate to consider when the decision to accept or reject the null hypothesis is not always firm. The natural, subjective interpretation of a p‐value as the probability that the null hypothesis is true is also examined. The usual asymptotic correspondence between these two probabilities for one‐sided hypotheses is shown to be strengthened when the standard p‐value is replaced by the mid‐p.
Cramér‐von Mises statistics for discrete distributions
Authors: Choulakian V. , Lockhart R.A. , Stephens M.A.
Published: June 2006

Cramér‐von Mises statistics are developed for use in testing for discrete distributions, and tables are given for tests for the discrete uniform distribution.
Robust weighted likelihood estimators with an application to bivariate extreme value problems
Authors: Dupuis Debbie J. , Morgenthaler Stephan
Published: June 2006

The authors achieve robust estimation of parametric models through the use of weighted maximum likelihood techniques. A new estimator is proposed and its good properties illustrated through examples. Ease of implementation is an attractive property of the new estimator. The new estimator downweights with respect to the model and can be used for complicated likelihoods such as those involved in bivariate extreme value problems. New weight functions, tailored for these problems, are constructed. The increased insight provided by our robust fits to these bivariate extreme value models is exhibited through the analysis of sea levels at two East Coast sites in the United Kingdom.