bluuebunny/crossref_metadata_2025_split huggingface dataset:
Strassen type limit points for moving averages of a wiener process
Authors: Chan A. H. C. , Csörgö M. , Révész P. 
Published: June 2006

AbstractLet {W(s); 8 ≥ 0} be a standard Wiener process, and let βN = (2aN (log (N/aN) + log log N)‐1/2, 0 < αN ≤ N < ∞, where αN↑ and αN/N is a non‐increasing function of N, and define γN(t) = βN[W(nN + taN) − W(nN)), 0 ≥ t ≥ 1, with nN = N – aN. Let K = {x ϵ C[0,1]: x is absolutely continuous, x(0) = 0 and

}. We prove that, with probability one, the sequence of functions {γN(t), t ϵ [0,1]} is relatively compact in C[0,1] with respect to the sup norm ||·||, and its set of limit points is K. With aN = N, our result reduces to Strassen's well‐known theorem. Our method of proof follows Strassen's original, direct approach. The latter, however, contains an oversight which, in turn, renders his proof invalid. Strassen's theorem is true, of course, and his proof can also be rectified. We do this in a somewhat more general context than that of his original theorem. Applications to partial sums of independent identically distributed random variables are also considered.
A note on the admissibility of hammersley's estimator of an integer mean
Authors: Khan Rasul A. 
Published: June 2006

AbstractLetX1,X2, …,Xnbe identically, independently distributedN(i,1) random variables, wherei= 0, ±1, ±2, … Hammersley (1950) showed that d = [X̄n], the nearest integer to the sample mean, is the maximum likelihood estimator ofi. Khan (1973) showed thatdis minimax and admissible with respect to zero‐one loss. This note now proves a conjecture of Stein to the effect that in the class of integer‐valued estimatorsdis minimax and admissible under squared‐error loss.
On two approximations to the F‐distribution: Application to testing for intraclass correlation in family studies
Authors: Donner Allan , Wells George A. , Eliasziw Michael 
Published: June 2006

AbstractTwo approximations to the F‐distribution are evaluated in the context of testing for intraclass correlation in the analysis of family data. The evaluation is based on a computation of empirical significance levels and a comparison between p‐values associated with these approximations and the corresponding exact p‐values. It is found that the approximate methods may give very unsatisfactory results, and exact methods are therefore recommended for general use.
Bayesian break‐point forecasting in parallel time series, with application to university admissions
Authors: Rubin D. B. , Stroud T. W. F. 
Published: June 2006

AbstractA regular supply of applicants to Queen's University in Kingston, Ontario is provided by 65 high schools. Each high school can be characterized by a series of grading standards which change from year to year. To aid admissions decisions, it is desirable to forecast the current year's grading standards for all 65 high schools using grading standards estimated from past year's data. We develop and apply a Bayesian break‐point time‐series model that generates forecasts which involve smoothing across time for each school and smoothing across schools. “Break point” refers to a point in time which divides the past into the “old past” and the “recent past” where the yearly observations in the recent past are exchangeable with the observations in the year to be forecast. We show that this model works fairly well when applied to 11 years of Queen's University data. The model can be applied to other data sets with the parallel time‐series structure and short history, and can be extended in several ways to more complicated structures.
Tests for the multivariate two‐sample problem based on empirical probability measures
Authors: Kim Kang‐Kyun , Foutz Robert V. 
Published: June 2006

AbstractNonparametric tests are proposed for the equality of two unknown p‐variate distributions. Empirical probability measures are defined from samples from the two distributions and used to construct test statistics as the supremum of the absolute differences between empirical probabilities, the supremum being taken over all possible events. The test statistics are truly multivariate in not requiring the artificial ranking of multivariate observations, and they are distribution‐free in the general p‐variate case. Asymptotic null distributions are obtained. Powers of the proposed tests and a competitor are examined by Monte Carlo techniques.
Uniform stochastic orderings and total positivity
Authors: Lynch James , Mimmack Gillian , Proschan Frank 
Published: June 2006

AbstractUniform stochastic orderings of random variables are expressed as total positivity (TP) of density, survival, and distribution functions. The orderings are called uniform because each is a stochastic order that persists under conditioning to a family of intervals—for example, the family consisting of all intervals of the form (‐∞,x]. This paper is concerned with the preservation of uniform stochastic ordering under convolution, mixing, and the formation of coherent systems. A general TP2 result involving preservation of total positivity under integration is presented and applied to convolutions and mixtures of distribution and survival functions. Log‐concavity of distribution, survival, and density functions characterizes distributions that preserve the various orderings under convolution. Likewise, distributions that preserve orderings under mixing are characterized by TP2 distribution and survival functions.
Limiting distributions of Kolmogorov‐Lévy‐type statistics under the alternative
Authors: Kozek Andrzej 
Published: June 2006

AbstractLet Xi, 1 ≤ i ≤ n, be independent identically distributed random variables with a common distribution function F, and let G be a smooth distribution function. We derive the limit distribution of □{ρα(Fn, G) ‐ α(F, G)}, where Fn is the empirical distribution function based on X1,…,Xn and α is a Kolmogorov‐Lévy‐type metric between distribution functions. For α ≤ 0 and two distribution functions F and G the metric pα is given by pα(F, G) = inf {ϵ ≤ 0: G(x ‐ αϵ) ‐ ϵ F(x) ≤ G(x + αϵ) + ϵ for all x ℝ}.
Invariant estimation of functions
Authors: Hooper Peter M. 
Published: June 2006

AbstractLet Z be a random variable taking values in a space ℒ︁ with unknown distribution indexed by θϵΩ, letψ:Ω × →[0, 1] be a given function, and consider the problem of estimating (θ, Z) with δ(Z), where the risk is θl(δ(Z)‐ψ(θ, Z)). The form of minimum‐risk invariant estimators is derived, and versions of the Rao‐Blackwell and Hunt‐Stein theorems are given. The results are applied in two areas: conditional properties of confidence and prediction regions, and the estimation of distribution functions, quantiles, and events.Soit Z une variable aleatoire prenant ses valeurs dans un espace ℒ︁ et dont la loi est indicée par un paramètre inconnu θϵΩ. Soit aussi θϵΩ, letψ:Ω × ℒ︁ →[0, 1] une application arbitraire, et supposons qu'on veuille estimer ψ(θ, Z) par une fonction δ deZ en minimisant le risque E l(δ(Z)‐ψ(θ, Z). Nous donnons ici la forme explicite des estimateurs invariants δ(Z) et nous adaptons les théorèmes de Rao‐Blackwell et de Hunt‐Stein à ce contexte. Nous appliquons ensuite nos résultats à deux problémes bien particuliers. Le premier concerne les propriétés conditionnelles des régions de confiance et de prédiction, tandis que le second a trait à l'estimation ďévénements, de quantiles ou de fonctions de répartition.
Curvature and linear rank statistics
Authors: Reid N. 
Published: June 2006

AbstractAn exact expression for the curvature (Efron, 1975) of the family of rank distributions is derived. This curvature is almost zero for many cases of practical interest. A simple formula (13) relates the rank curvature to the curvature of the underlying density. Some implications of this result are discussed.L'auteure développe une formule permettant de calculer de facon explicite la courbure (voir Efron, 1975) de la famille des distributions de rang. II s'avère notamment que cette courbure est presque nulle dans un grand nombre de cas pratiques. Une formule assez simple (13) permet par ailleurs de mettre en évidence la relation qu'il existe entre la courbure de rang et celle de la fonction de densité sous‐jacente. Quelques‐unes des consequénces de ce resultat font l'objet ďune discussion.
A regression method for censored inverse‐Gaussian data
Authors: Whitmore G. A. 
Published: June 2006

AbstractMultiple regression methods are considered for progressively right‐censored inverse‐Gaussian data. Maximum‐likelihood estimators are derived using the EM algorithm, and their asymptotic distributional properties are presented. The methodology is demonstrated using two case illustrations, one of which involves the defective feature of the inverse‐Gaussian distribution. The relationship of the methodology to regression methods for complete inverse‐Gaussian samples and to other regression methods for censored survival data is discussed.
Universal optimality of experimental designs: Definitions and a criterion
Authors: Bondar James V. 
Published: June 2006

AbstractSeveral definitions of universal optimality of experimental designs are found in the Literature; we discuss the interrelations of these definitions using a recent characterization due to Friedland of convex functions of matrices. An easily checked criterion is given for a design to satisfy the main definition of universal optimality; this criterion says that a certain set of linear functions of the eigenvalues of the information matrix is maximized by the information matrix of a design if and only if that design is universally optimal. Examples are given; in particular we show that any universally optimal design is (M, S)‐optimal in the sense of K. Shah.
An ordering of dependence for distribution of k‐tuples, with applications to lotto games
Authors: Joe Harry 
Published: June 2006

AbstractA majorization ordering is defined over the class of distributions of k‐tuples from (1,…,N) with the same vector of marginal frequencies of occurrences for the integers from 1 to N. Results are obtained for the maximal and minimal distributions with respect to this ordering. Applications to lotto games and election results are presented; for Lotto 6/49, an estimate of the distribution of 6‐tuples is given, based on data on the marginal frequencies of the numbers 1 to 49.On s'intéresse à la classe des distributions de k‐tuplets formés d'entiers choisis parmi (1,…,N) qui présentent un vecteur commun de fréquences d'apparition marginales pour chaque entier 1,…,N. On y définit un ordre de majoration et on obtient certains résultats en ce qui a trait aux distributions maximale et minimale induites par cet ordre. On présente quelques applications dans le domaine des jeux de lotto et des résultats d'élection. En ce qui concerne le Lotto 6/49, on fournit une estimation de la distribution des 6‐tuplets en se basant sur des données relatives aux fréquences marginales des nombres 1 à 49.
Heuristic approach to some laws for Brownian motion
Authors: Imhof J. P. 
Published: June 2006

AbstractCsàki and Vincze have shown that for an elementary tied‐down random walk, the pair (maximum, instant of maximum) has the same law as (time spent in (0, 1/2), time spent above 1/2). Formal passage to the limit indicates that the former pair has for a Brownian bridge the same law as (local time at 0, duration of positivity). A quadrivariate density of Karatzas and Shreve and an equivalence for Brownian motion with drift follow.
A product‐limit estimator for use with length‐biased data
Authors: Winter B. B. , Földes A. 
Published: June 2006

AbstractThe following life‐testing situation is considered. At some time in the distant past, n objects, from a population with life distribution F, were put in use; whenever an object failed, it was promptly replaced. At some time τ, long after the start of the process, a statistician starts observing the n objects in use at that time; he knows the age of each of those n objects, and observes each of them for a fixed length of time≪ ∞, or until failure, whichever occurs first. In the case where T is finite, some of the observations may be censored; in the case where T =∞, there is no censoring. The total life of an object in use at time ∞ is a length‐biased observation from F. A nonparametric estimator of the (cumulative) hazard function is proposed, and is used to construct an estimator of F which is of the product‐limit type. Strong uniform consistency results (for n → ∞) are obtained. An “Aalen‐Johansen” identity, satisfied by any pair of life distributions and their (cumulative) hazard functions, is used in obtaining rate‐of‐convergence results.
On the rate of convergence of recursive kernel estimates of probability densities
Authors: Abdul‐Al K. I. 
Published: June 2006

AbstractRecursive estimates fnr(x)of the rth derivative fr(x)(r=0,1)of the univariate probability density f(x) for strictly stationary processes {Xj,} are considered. The asymptotic variance‐covariance of fnr(x)is established for stationary triangular arrays of random variables satisfying various asymptotic independence‐uncorrelatedness conditions.
A characterization of the power function distribution
Authors: Ahsanullah M. , Kabir A.B.M.Lutful 
Published: June 2006

AbstractSuppose that in a random sample of size n from a population with probability density function f(x), the order statistics are X(1) < X(2) < … < X(n). It is proved that a necessary and sufficient condition for f(x) to be the density function of the power function distribution is that the statistics X(r)/X(s) and X(t) (1 ≤ r < s < t ≤ n) are independent.
On equalities between BLUES, WLSEs, and SLSEs
Authors: Baksalary J. K. , Kala R. 
Published: June 2006

AbstractNecessary and sufficient conditions for equalities between the best linear unbiased estimator, the weighted least‐squares estimator, and the simple least‐squares estimator of the expectation vector in a general Gauss‐Markoff model are given in some alternative formulations. The main result states, somewhat surprisingly, that the weighted least‐squares estimator cannot be identical with the simple least‐squares estimator unless they both coincide with the best linear unbiased estimator.
Some new classification rules forcunivariate normal populations
Authors: Gupta A. K. , Govindarajulu Z. 
Published: June 2006

AbstractIn this paper we propose classification rules with respect to the mean, variance, and the coefficient of variation forc(≥2)univariate normal populations. Two different approaches to the problem have been studied (a) where the probability of correct classification is at least a pre‐assigned numberp*(l/c ≤ p* < 1), and(b)where the probability of correct classification has to be evaluated. For the two approaches(a)and(b), classification rules with respect to the mean have been studied when thecpopulations have(i)common known variance,(ii)common unknown variance. The classification rules of approach(b)in the case of common known or unknown variance is also valid when the variances are not all equal and are known or unknown. Classification rules with respect to the coefficient of variation are also given for the two approaches when the population parameters are unknown. Classification rules with respect to the variance for the two approaches are explored when the means are unknown. In each case of approach(b), the classification rule has been shown to possess a certain optimum property.
Certain properties of bivariate distributions associated with generalized hypergeometric functions
Authors: Saxena R. K. , Sethi P. L. 
Published: June 2006

AbstractThe object of this paper is to introduce certain properties of three new types of statistical distributions associated with generalized hypergeometric functions. The generalized phase and radial density functions associated with these distributions are obtained by making use of either characteristic functions or weighted‐mixture representations, where the independent x and y component distributions are not necessarily the same. 0nly bivariate situations are investigated explicitly. However, the results can be extended to multivariate cases by adopting a similar procedure. The results given recently by McNolty and Tomsky follow as special cases of the results of this paper.
Strong uniform consistency of integrals of density estimators
Authors: Winter B. B. 
Published: June 2006

AbstractThroughout this note, (Xj) is a sequence of independent and identically distributed random variables, defined on a probability space (Ω, ℑ ρ) and having common distribution F. It is shown that if the cumulative distribution function (or cdf) F is continuous, and F(x)=N−1 Σ uN(x‐Xj) where (uN) is a sequence of cdf's converging weakly to the cdf of the unit mass at zero, and F almost surely converges uniformly to F. This result implies that if F has a density f and fN is a typical nonparametric density estimator and FN(x) = ∫ fN(t)dt then, with probability one, FN converges uniformly to F.
On testing latent vectors of a normal covariance matrix
Authors: Gupta Rameshwar D. 
Published: June 2006

AbstractLet x' = (x1,…, xp) have a normal distribution with mean vector zero and covariance matrix Σ. Then Kshirsagar [(1961), (1966)] gives a criterion for testing the hypothesis that a single latent vector of Σ has a specified direction. Here we generalize Kshirsagar's results to the simultaneous testing of more than one vector.
On the distribution of hand patterns in bridge: Man‐dealt versus computer‐dealt
Authors: Berger Paul D. 
Published: June 2006

AbstractThis note tries to answer the complaint that the computer‐dealt hands, in bridge tournaments, seem to break too often in an unusual manner and that hand patterns are biased toward hands with long suits. Results of some empirical studies on computer‐dealt and man‐dealt hands are reported in this article.
An investigation of first‐order and second‐order designs for extrapolation outside a hypersphere
Authors: Draper Norman R. , Herzberg Agnes M. 
Published: June 2006

AbstractMethods for selecting a first‐order or second‐order rotatable response surface design when both variance and bias error exist are applied to a situation in which it is desired to extrapolate the fitted model in all directions outside of a sphere within which all the experiments are to be made. The extrapolation region is a spherical shell.
Approximate conditional inference for location familles
Authors: Diciccio Thomas J. 
Published: June 2006

AbstractApproximations to exact conditional inference for location familles are considered. Methods which improve the standard normal and chi‐squared approximations to the conditional distributions of pivots arising in standard large‐sample theory are discussed, including the use of parameter transformations for parametrization‐dependent pivots, and the use of scaling factors for the likelihood‐ratio statistic. The methods are illustrated and compared in a series of examples.
Some joint distributions for conditional random walks
Authors: Csáki E. , Mohanty S. G. 
Published: June 2006

AbstractJoint distributions concerning maxima, minima, and their indices are determined for certain conditional random walks called Bernoulli excursion and Bernoulli meander. The distribution of the local time of these processes is treated by generating function technique. Limiting distributions are also given, providing some partial results for Brownian excursion and meander.
Comparison of estimators of interclass and intraclass correlations from familial data
Authors: Srivastava M. S. , Katapa R. S. 
Published: June 2006

AbstractWhen familles have different numbers of offspring, Srivastava (1984) gave an alternative approach to deriving the maximum‐likelihood estimators of inter‐ and intraclass correlations, which requires solving only one equation. Since the procedure is iterative and requires considerable computation, several alternative estimators have been proposed in the literature. In this paper, a comparison is made between the maximum‐likelihood estimator and two alternative estimators proposed by Srivastava (1984). By obtaining the asymptotic normal distributions of the estimators, it is shown that one of the easily computable estimators is comparable to the maximum‐likelihood estimator.
The superharmonic condition for simultaneous estimation of means in exponential familles
Authors: Haff L. R. , Johnson R. W. 
Published: June 2006

AbstractThe mean vector associated with several independent variates from the exponential subclass of Hudson (1978) is estimated under weighted squared error loss. In particular, the formal Bayes and “Stein‐like” estimators of the mean vector are given. Conditions are also given under which these estimators dominate any of the “natural estimators”.Our conditions for dominance are motivated by a result of Stein (1981), who treated the Np (θ, I) case with p ≥ 3. Stein showed that formal Bayes estimators dominate the usual estimator if the marginal density of the data is superharmonic. Our present exponential class generalization entails an elliptic differential inequality in some natural variables.Actually, we assume that each component of the data vector has a probability density function which satisfies a certain differential equation. While the densities of Hudson (1978) are particular solutions of this equation, other solutions are not of the exponential class if certain parameters are unknown. Our approach allows for the possibility of extending the parametric Stein‐theory to useful nonexponential cases, but the problem of nuisance parameters is not treated here.
The exact distribution of the ratio of a linear combination of chi‐square variables over the root of a product of chi‐square variables
Authors: Provost Serge B. 
Published: June 2006

AbstractThis article gives the exact distribution of a statistic whose numerator and denominator are independent, the former being a linear combination of independent chi‐square variables and the latter being thekth root of a product ofkindependent chi‐square variables. This structure appears in the study of multivariate linear functional relationship models. The technique of the inverse Mellin transform is used in order to obtain the density of this test statistic in a computable form.
Geostochastic calculus
Authors: Dawson D.A. 
Published: June 2006

AbstractA stochastic calculus for a family of continuous measure‐valued Markov processes is developed. Such processes arise naturally in the construction of stochastic models of spatially distributed populations. The stochastic calculus is a tool whereby a class of density‐dependent models can be studied in terms of the multiplicative measure diffusion process. In this paper the stochastic integral is introduced in the space‐time setting and a Cameron‐Martin‐Girsanov theorem is established.
A class of tests for testing ‘new is better than used’
Authors: Koul Hira L. 
Published: June 2006

AbstractA class of tests is proposed for testing H0 F̄(x) = e−λx, λ > 0, x≥0 vs. H1 F̄(x + y) ≤ F̄(x)F̄(y), x, y≥0, with strict inequality for some x, y ≥ 0 (F = new is better than used). Efficiency comparisons of some tests within the class are made and a new test is proposed on the basis of these comparisons. Consistency and the asymptotic normality of the class of tests is proved under fairly broad conditions on the underlying entities.
The variability of rainfall acidity revisited
Authors: Nhu Le D. , Petkau A. John 
Published: June 2006

AbstractSix years of rainfall‐event pH measurements from the nine‐station MAP3S/PCN monitoring network in the eastern United States were analyzed. The initial objective was an attempted validation of the model developed by Eynon and Switzer (1983, Canad. J. Statist. 11, 11–24) on this independent data set. Because some features of the structure presumed in the model are not evident in this data set, the underlying structure of the data was then explored in some detail. Both aspects of the investigation confirmed that the identification of an appropriate statistical model for such data is a difficult undertaking; anticipated structure may not be evident, and the data corresponding to specific stations or years may exhibit anomalous behavior.