bluuebunny/crossref_metadata_2025 huggingface dataset:
Uniform stochastic orderings and total positivity
Authors: Lynch James , Mimmack Gillian , Proschan Frank
Published: June 2006

Uniform 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

Let 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

Let 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

An 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

Multiple 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

Several 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.
A robust alternative to the normal distribution
Authors: McLeish D. L.
Published: June 2006

A wider‐tailed family of distributions is suggested as an alternative to the normal distribution having many of the desirable properties of the normal family. One advantage of this alternative is the greater robustness of maximum‐likelihood estimates.
Negative binomial and mixed Poisson regression
Authors: Lawless Jerald F.
Published: June 2006

A number of methods have been proposed for dealing with extra‐Poisson variation when doing regression analysis of count data. This paper studies negative‐binomial regression models and examines efficiency and robustness properties of inference procedures based on them. The methods are compared with quasilikelihood methods.
An ordering of dependence for distribution of k‐tuples, with applications to lotto games
Authors: Joe Harry
Published: June 2006

A 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

Csàki 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

The 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

Recursive 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.
Prediction Limit for Observation from the Exponential Distribution
Authors: Takada Yoshikazu
Published: June 2006

Prediction limits for the observation from the exponential distribution are considered. Introducing a risk function to compare prediction limits, the limit which minimizes it among the class of α‐invariant prediction limits is obtained.
A characterization of the power function distribution
Authors: Ahsanullah M. , Kabir A.B.M.Lutful
Published: June 2006

Suppose 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.
Classes Inférieures de suites gaussiennes asymptotiquement indépendantes
Authors: Wong H. S. F.
Published: June 2006

In this paper we prove a theorem on “asymptotically independent” Gaussian sequences. This result improves and simplifies a result of Lai (1973) on lower classes of Gaussian sequences.
On equalities between BLUES, WLSEs, and SLSEs
Authors: Baksalary J. K. , Kala R.
Published: June 2006

Necessary 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

In 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

The 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.
A probability model for inter‐birth interval
Authors: George A.
Published: June 2006

This paper deals with the study of probability models for inter‐birth intervals. Expressions for the first four moments have been obtained under general probability distributions for the various components of the inter‐birth interval. The exact probability distribution of the inter‐birth interval has been obtained for a continuous case.
Strong uniform consistency of integrals of density estimators
Authors: Winter B. B.
Published: June 2006

Throughout 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

Let 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

This 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

Methods 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

Approximations 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

Joint 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

When 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

The 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

This 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

A 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.
Measuring diversity in biological populations with logarithmic abundance distributions
Authors: Wani Jagannath K.
Published: June 2006

Fisher's logarithmic distribution for species abundance is derived under a suitable set of conditions. The derivation explains the explicit meaning of the two parameters of the distribution.
A class of tests for testing ‘new is better than used’
Authors: Koul Hira L.
Published: June 2006

A 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

Six 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.
Interval estimates for diatom‐inferred lake pH histories
Authors: Oehlert Gary W.
Published: June 2006

We investigate ordinary least‐squares and Bayesian methods for constructing interval estimates for historical lake pH's inferred from diatom sediments. The Bayesian method explicitly models several forms of variability, including the sampling and classification variability of the diatom records, estimation variability, and measurement error in observed pH's. The two methods produce similar interval estimates, but the Bayesian model allows design recommendations to be made.
Nonparametric testing for time series: A bibliography
Authors: Dufour Jean‐Marie , Lepage Yves , Zeidan Hanna
Published: June 2006

This bibliography brings together and classifies a wide variety of nonparametric methods which are pocentially useful for the analysis of time series data, in particular for testing randomness. Inference on Markov chain models is also extensively surveyed.
Change‐over designs with complete balance for first and second residual effects
Authors: Sharma V.K.
Published: June 2006

This paper presents a unified method of constructing change‐over designs that permit the estimation of direct effects orthogonal to all other effects when the residual effects of treatments last for two consecutive periods. Explicit methods of analysis of these designs have been obtained for the situations where the first period observations are omitted from the analysis and where the first period observations are included.
The random robin problem for laplace's equation
Authors: Becus Georges A.
Published: June 2006

A random generalized solution to the Robin problem for Laplace's equation is defined in terms of the sections of the random boundary data. Existence, uniqueness, and properties are established for such a solution. Particularizations to the Dirichlet and Newmann problems as well as generalization to the Robin‐Poisson problem are mentioned. Applications of the results are provided.
The non‐null distribution for the problem of tests of independence
Authors: Pederzoli G.
Published: June 2006

The problem of testing independence in the multinormal case is considered in this paper. The non‐null distribution of the likelihood ratio criterion is obtained for the case of two subvectors by using a simple straightforward technique. The null case as well as the known cases are also verified.
The mean and variance of rank and exponential score product moment statistics in the non‐circular case
Authors: Rodden B. E. , Landolt J. P.
Published: June 2006

This paper gives a general formula for the first two moments of the non‐circular product moment statistic, which is used as a test for the statistical independence of the interarrival times of certain time series data, e.g., neuronal spike discharges. For the special cases of rank and exponential score product moment statistics, the mean and variance are formulated.
Bounds for moments through a general orthogonal expansion in a pre‐hilbert space‐I
Authors: Mathai A. M.
Published: June 2006

Bounds are obtained for the product moments of an arbitrary finite number of ordered random variables. These bounds are obtained with the help of a representation of an arbitrary function in terms of a complete orthonormal system in a pre‐Hilbert space of square integrable functions defined in a k‐dimensional unit cube.
Multiparameter estimation of discrete exponential distributions
Authors: Tsui Kam‐Wah
Published: June 2006

LetX1, …,Xpbe independent random variables, all having the same distribution up to a possibly varying unspecified parameter, where each of thepdistributions belongs to the family of one parameter discrete exponential distributions. The problem is to estimate the unknown parameters simultaneously. Hudson (1978) shows that the minimum variance unbiased estimator (MVUE) of the parameters is inadmissible under squared error loss, and estimators better than the MVUE are proposed. Essentially, these estimators shrink the MVUE towards the origin. In this paper, we indicate that estimators shifting the MVUE towards a point different from the origin or a point determined by the observations can be obtained.
Estimation of poisson means under weighted squared error loss
Authors: Tsui Kam‐Wah
Published: June 2006

In estimating the means of several independent Poisson distributions, we show that the maximum likelihood estimator is inadmissible when general weighted squared error loss is the criterion. Using this result, we extend the known results on estimation of several Poisson means (Peng 1975, Hudson 1978) to the case where possibly more than one observation is taken from each Poisson distribution and the samples are not necessarily of the same size.
Tests based on equivariant estimators
Authors: Rivest Louis‐Paul
Published: June 2006

Let Ť(1) and Ť(2) be location‐equivariant estimators of an unknown location parameter μ. It is shown that the test for H0: μ ≤ μ0 versus HA : μ > μ0 that rejects H0 if Ť(1) is large is uniformly more powerful than the one that rejects H0 if Ť(2) is large if and only if Ť(2) is “more dispersed” than Ť(1). A similar result is obtained for tests on scale using the star‐shaped ordering. Examples are given.
On Khatri's characterization of the inverse‐Gaussian distribution
Authors: Letac GÉRard , Seshadri Vanamamalai
Published: June 2006

Khatri has given a characterization of the inverse‐Gaussian distribution by the independence of two statistics. His proof involves assumptions on the existence of certain moments. In this note, we offer a short proof using only the positivity of the random variable X1.
Mixtures, embedding, and ancillarity
Authors: Evans M. , Fraser D. A. S. , Monette G.
Published: June 2006

Ancillary statistics, proposed by Fisher (1925), can be constructed by forming amixture model(Birnbaum 1962) or can be extracted or derived from atransformation‐parameter model(Peisakoff 1951, Fraser 1961) or from the corresponding error‐basedstructural model(Fraser 1968, 1979); these latter models involve an implicitmixturestructure. Compound models with ancillaries can also be formed by a crossembedding, discussed from a technical viewpoint in this paper. Of the 25 examples in Buehler (1982), 22 are mixtures or implicit mixtures and 3 correspond to cross embedding. The cross embedding examples exemplify the nonuniqueness difficulties with ancillaries. This paper discusses a simple and two generalized versions of cross embedding but makes no general valuations of these for statistical inference; their role within inference is discussed in Evans, Fraser, and Monette (1984, 1985).
Analyzing cross‐sectional and longitudinal lung‐function measurements: The effects of age
Authors: Schulzer Michael , Enarson Donald A. , Chan‐Yeung Moira
Published: June 2006

The problem of interpreting lung‐function measurements in industrial workers is examined. The data under discussion pertain to FEV1 and FVC measurements in smoking and in nonsmoking groups of grain‐elevator workers in British Columbia and of workers in Vancouver City Hall. Initial observations have now been enriched by longitudinal follow up data on the same groups after three and after six years. It is shown that interesting selection phenomena, favouring “fit” individuals, take place over time, with regard both to lung symptoms and lung functions. Thus cross‐sectional and longitudinal studies refer to somewhat different populations. It also appears that longitudinal studies are considerably more sensitive to identifying cumulative lung damage than are corresponding cross‐sectional studies. The nonlinearity of the effect of age on lung functions is noted in the longitudinal data in a number of cases, lending support to the hypothesis of association between quadratic age effect and cumulative exposure to lung insults.
Testing whether new is better than used of a specified age, with randomly censored data
Authors: Hollander Myles , Park Dong Ho , Proschan Frank
Published: June 2006

Using randomly censored data, we develop a test of the null hypothesis that a new item has stochastically the same residual lifelength as does a used item of specified age t0, versus the alternative hypothesis that a new item has stochastically greater residual lifelength than does a used item of age t0. We also compare our test with a related test, developed for a complete‐data model, in order to study the loss in efficiency because of censoring.
Quadratic nuisance‐parameter‐free goodness‐of‐fit tests in the presence of location and scale parameters
Authors: Aly Emad‐Eldin A. A. , CsÖ MiklÓS
Published: June 2006

The asymptotic theory of a quadratic nuisance‐parameter‐free goodness‐of‐fit procedure is studied. The present techniques are applied in testing for the exponential, the logistic, the extreme value, and the Weibull distributions.
Equally spaced design points in polynomial regression: A comparison of systematic sampling methods with the optimal design of experiments
Authors: Bellhouse David R. , Herzberg Agnes M.
Published: June 2006

In some situations an experimenter may desire to have equally spaced design points. Three methods of obtaining such points on the interval [—1,1]—namely systematic random sampling, centrally located systematic sampling, and a purposive systematic sampling method which includes the endpoints ‐ 1 and 1 as two of the design points‐are evaluated under the D‐optimal and G‐optimal criteria. These methods are also compared to the optimal designs in polynomial regression and to the limiting designs of Kiefer and Studden (1976).
Predicting Pareto and exponential observables
Authors: Geisser Seymour
Published: June 2006

The author considers, from a Bayesian viewpoint, the problem of predicting a future fraction of observables that lie in a set when the present and future observables are Pareto‐distributed. Exact solutions as well as convenient approximations are obtained for the censored case.
Bayes and empirical Bayes shrinkage estimation of regression coefficients
Authors: Nebebe Fassil , Stroud T. W. F.
Published: June 2006

For a moderate or large number of regression coefficients, shrinkage estimates towards an overall mean are obtained by Bayes and empirical Bayes methods. For a special case, the Bayes and empirical Bayes shrinking weights are shown to be asymptotically equivalent as the amount of shrinkage goes to zero. Based on comparisons between Bayes and empirical Bayes solutions, a modification of the empirical Bayes shrinking weights designed to guard against unreasonable overshrinking is suggested. A numerical example is given.
Predictive densities and selection with genetic applications
Authors: Tallis G. M.
Published: June 2006

A set ofppopulations is subjected to a first sampling. From this, it is required to select one of the populations so that the mean of a future sample is maximized. Extensions to this problem are discussed and solved by the use of predictive densities. These results are finally adapted to populations with covariate structure under systems of balanced sampling. Applications to quantitative genetics are indicated.
Single‐parameter inference based on partial prior information
Authors: Lambert Diane , Duncan George T.
Published: June 2006

Partial specification of a prior distribution can be appealing to an analyst, but there is no conventional way to update a partial prior. In this paper, we show how a framework for Bayesian updating with data can be based on the Dirichlet(a) process. Within this framework, partial information predictors generalize standard minimax predictors and have interesting multiple‐point shrinkage properties. Approximations to partial‐information estimators for squared error loss are defined straightforwardly, and an estimate of the mean shrinks the sample mean. The proposed updating of the partial prior is a consequence of four natural requirements when the Dirichlet parameter a is continuous. Namely, the updated partial posterior should be calculable from knowledge of only the data and partial prior, it should be faithful to the full posterior distribution, it should assign positive probability to every observed event {X,}, and it should not assign probability to unobserved events not included in the partial prior specification.
On the characteristic function of multivariate Student t‐distribution
Authors: Sutradhar Brajendra C.
Published: June 2006

The characteristic function of the multivariate Student t‐distribution is obtained, and it is shown that this characteristic function has the pedogogical virtue of reducing the multivariate problem to the analogous univariate problem. Applications of the characteristic function are discussed.
Selecting a power‐series distribution for goodness of fit
Authors: Wani Jagannath K. , Lo Hing‐Po
Published: June 2006

The binomial, Poisson, logarithmic, negative binomial, and extended negative binomial distributions are characterized in the class of power‐series distributions (1) through a differential equation based on the ratio of two successive derivatives of the series function, (2) through the ratio of two probabilities associated with two successive values in the range of the random variable, and (3) through the ratio of two consecutive factorial moments. The ratios referred to in (2) and (3) above can be utilized to discriminate between the five power‐series distributions mentioned at the beginning.
Discrete approximations to the Csiszár, Renyi, and Fisher measures of information
Authors: Zografos K. , Ferentinos K. , Papaioannou T.
Published: June 2006

The problem of loss of information due to the discretization of data and its estimate is studied for various measures of information. The results of Ghurye and Johnson (1981) are generalized and supplemented for the Csiszár and Renyi measures of information as well as for Fisher's information matrix.
Slepian's inequality via the central limit theorem
Authors: Huffer Fred W.
Published: June 2006

We define a partial ordering of distributions which is preserved under convolutions and scale transformations. Some properties of this partial ordering are developed and then used to give a new argument for Slepian's inequality (1962).
The geometry of case deletion and the assessment of influence in nonlinear regression
Authors: Ross William H.
Published: June 2006

Numerous influence measures are available for use in linear regression. By contrast, very little has been done for nonlinear models. A notable exception is Chapter 4 of Cook and Weisberg (1982). The extension of measures based on case deletion from the linear to the nonlinear model usually involve linear approximation. In this paper, the geometry of case deletion is studied with a view to assessing the adequacy of linear approximation in the construction of influence measures for nonlinear regression. Of particular interest is the adequacy of the one‐step estimator for the jack‐knifed pseudoestimates of the unknown parameter vector.
Connectedness of PBIB designs
Authors: Baksalary Jerzy K. , Tabis Zenon
Published: June 2006

A necessary and sufficient condition for the connectedness of an m‐associate‐class PBIB design is derived in a form, and using an approach, different from those in Ogawa, Ikeda, and Kageyama (1984) and Saha and Kageyama (1984). The applicability of this condition is shown in the context of group‐divisible m‐associate‐class PBIB designs.
On the asymptotic efficiency of certain correlation tests of fit
Authors: McLaren C. G. , Lockhart Richard
Published: June 2006

Tests of fit based on correlation‐type statistics are investigated for the exponential, extreme‐value, and logistic distributions. The statistics are shown to be asymptotically normal at the rate log½n. The result is used to show that such tests have 0 asymptotic relative efficiency.
Bootstrapping regression models with BLUS residuals
Authors: Grenier Michèle , Léger Christian
Published: June 2006

To bootstrap a regression problem, pairs of response and explanatory variables or residuals can be resam‐pled, according to whether we believe that the explanatory variables are random or fixed. In the latter case, different residuals have been proposed in the literature, including the ordinary residuals (Efron 1979), standardized residuals (Bickel & Freedman 1983) and Studentized residuals (Weber 1984). Freedman (1981) has shown that the bootstrap from ordinary residuals is asymptotically valid when the number of cases increases and the number of variables is fixed. Bickel & Freedman (1983) have shown the asymptotic validity for ordinary residuals when the number of variables and the number of cases both increase, provided that the ratio of the two converges to zero at an appropriate rate. In this paper, the authors introduce the use of BLUS (Best Linear Unbiased with Scalar covariance matrix) residuals in bootstrapping regression models. The main advantage of the BLUS residuals, introduced in Theil (1965), is that they are uncorrelated. The main disadvantage is that only n —p residuals can be computed for a regression problem with n cases and p variables. The asymptotic results of Freedman (1981) and Bickel & Freedman (1983) for the ordinary (and standardized) residuals are generalized to the BLUS residuals. A small simulation study shows that even though only n — p residuals are available, in small samples bootstrapping BLUS residuals can be as good as, and sometimes better than, bootstrapping from standardized or Studentized residuals.
Seasonal adjustment in the eighties: Some problems and solutions
Authors: Dagum Estela Bee , Huot Guy , Morry Marietta
Published: June 2006

Statistics Canada, like most statistical bureaus, is concerned with problems affecting the accuracy, the consistency, and the usefulness of seasonally adjusted series. The most serious problems affecting the accuracy of seasonally adjusted data in the eighties are related to changes in trading‐day variations caused by changes in consumers' patterns and to the effect of the early arrival of Easter in March (1986) and the beginning of April (1980, 1983, 1985, 1988). The problems affecting consistency mainly result from the lack of uniform practices for the seasonal adjustment of related series and economic aggregates. This lack of uniformity is present in (1) the seasonal adjustment of current observations, which can be done by applying the X‐11‐ARIMA program in four different modes; and (2) the seasonal adjustment of key economic and social indicators, which are aggregates and give different results if adjusted directly or indirectly (through the aggregation of each seasonally adjusted component). Finally, the problem of usefulness of seasonally adjusted data manifests itself for series that are largely irregular, posing then the need for further smoothing.
A look at response errors in the labour force survey
Authors: Lemaitre Georges
Published: June 2006

In conducting surveys, survey‐takers impose upon respondents certain cognitive and perceptual tasks the difficulty of which will depend upon a variety of factors. This paper examines the types of questions asked in the Canadian Labour Force Survey with an eye to assessing their “difficulty” and to identifying covariates of difficulty, with respect to both the nature of the information sought and the circumstances of the reinterview. The conclusions are extended to retrospective surveys, where response errors often lead to estimates that are seriously biased.
Parameter estimation under orthant restrictions
Authors: Fernández Miguel A. , Rueda Cristina , Salvador Bonifacio
Published: June 2006

The authors consider the estimation of linear functions of a multivariate parameter under orthant restrictions. These restrictions are considered both for location models and for the Poisson distribution. For these models, situations are characterized for which the restricted maximum likelihood estimator dominates the unrestricted one for the estimation of any linear function of the parameter. The results obtained point directly to the importance of the dimension of the parameter space, the central direction of the cone and its vertex in these cases. Special attention is given to examples, such as the one‐way analysis of variance, where the estimation of individual interesting linear functions of the parameter, as the coordinates and the differences between them, is also treated.
A brand share model for Canadian cigarettes
Authors: Sherif F. , Thompson Mary E.
Published: June 2006

In an attempt to gain some insight into the way in which advertising affects the distribution of sales with different brands, a brand share model for Canadian filter cigarette brands is presented, using Canadian data for the period 1967‐1975.
On Hacking's fiducial theory of inference
Authors: Sharma Shyam S.
Published: June 2006

Fisher's theory of fiducial inference is known to lead to mathematical inconsistencies. Hacking (1965) puts forward a new basis for fiducial inference. In this paper we have presented Hacking's theory retaining his original terminology but replacing his notation by more usual mathematical notation. His condition of irrelevance is derived in an explicit mathematical form, making it more comprehensible to statisticians. Further an example is constructed to show that Hacking's theory also leads to mathematical inconsistencies.
Deficiencies of minimum discrepancy estimators
Authors: Ponnapalli R.
Published: June 2006

Suppose the multinomial parameterspr(θ) are functions of a real valued parameter 0,r= 1,2, …,k.A minimum discrepancy (m.d.) estimator θ of θ is defined as one which minimises the discrepancy functionD= Σnrf(pr/nr), for a suitable functionfwherenris the relative frequency inr‐th cell,r=1,2, …, k.All the usual estimators like maximum likelihood (m. l), minimum chi‐square (m. c. s.)., etc. arem.d.estimators. Allm.d.estimators have the same asymptotic (first order) efficiency. They are compared on the basis of their deficiencies, a concept recently introduced by Hodges and Lehmann [2]. The expression for least deficiency at any θ is derived. It is shown that in general uniformly least deficient estimators do not exist. Necessary and sufficient conditions onpr(0) form. t.andm. c. s.estimators to be uniformly least deficient are obtained.
Estimation of distribution parameters in time mortality trials: An example of time mortality analysis
Authors: Lampkin H. , Ogawa J.
Published: June 2006

In this paper we are primarily concerned with the effectiveness of a particular insecticide on beetles. The statistical problem is the comparison of results calculated by the standard probit method adapted to the time‐mortality curve and those calculated by a suitably selected set of sample quantiles.
The design of a clinical trial when there are two categories of patients
Authors: Donner Allan
Published: June 2006

Strategies are investigated for selecting one of two medical treatments when patients may be stratified into two distinct categories on the basis of their expected difference in response to the two treatments. The relative effectiveness of the following three strategies are assessed: (1) separate decisions made independently for the two categories, (2) a single overall decision made on the basis of simple pooling, and (3) the Bayes strategy.
Testing equality of several exponential distributions
Authors: Shah S. M. , Rathod V. R.
Published: June 2006

Roy's union‐intersection principle is used to develop a test procedure to test the equality of scale parameters of several exponential distributions. Upper five and one percent values of the test statistic for two and three exponential distributions are tabulated and an illustrative simulated example is qiven.
Bayes two‐decision procedures for two‐sample problems and rank‐order data
Authors: Baskerville J. C. , Solomon D. L.
Published: June 2006

A two‐sample problem for rank‐order data is formulated as a two‐decision problem. Using the general Bayes solution, Bayes procedures are derived for several configurations of the set of states of nature including some for which the problem is distribution‐free. It is shown that for certain prior distributions these procedures reduce to classical LMP rank tests. Some devices for selection of prior distributions are suggested. It is shown that the Bayes risk of these procedures tends to zero as sample sizes increase.
On the construction of group divisible incomplete block designs
Authors: Trivedi H. T. , Sharma V. K.
Published: June 2006

In this paper a method of constructing group‐divisible incomplete block designs has been suggested. A series of balanced incomplete block designs has also been obtained.
Autoregressive moving‐average convolution processes on the unit circle
Authors: Zwiers F. W.
Published: June 2006

ARMA convolution models for processes in continuous space (in this case the unit circle) and discrete time are derived as a natural extension of the usual Box‐Jenkins models. Both weakly time‐stationary and nonstationary processes are considered. Sufficient conditions for the existence of weakly time‐stationary ARcMAc processes are derived, and the covariance functions for some processes are computed. It is demonstrated that the usual scalar and multivariate ARMA processes can be embedded within the larger class of ARCMAc models. A possible application of these models to sea‐surface temperature prediction is discussed.
A class of time‐reversible semi‐Markov processes
Authors: Schaufele Ronald A.
Published: June 2006

In this paper, we investigate a class of semi‐Markov processes, first touched upon lightly in Pyke and Schaufele (1966), that are time‐reversible. Results that are difficult to prove for semi‐Markov processes in general are often made more simple for time‐reversible semi‐Markov processes, and some examples are given.
Asymptotic spacings theory with applications to the two‐sample problem
Authors: Holst Lars , Rao J. S.
Published: June 2006

The asymptotic distribution theory of test statistics which are functions of spacings is studied here. Distribution theory under appropriate close alternatives is also derived and used to find the locally most powerful spacing tests. For the two‐sample problem, which is to test if two independent samples are from the same population, test statistics which are based on “spacing‐frequencies” (i.e., the numbers of observations of one sample which fall in between the spacings made by the other sample) are utilized. The general asymptotic distribution theory of such statistics is studied both under the null hypothesis and under a sequence of close alternatives.