bluuebunny/crossref_metadata_2025 huggingface dataset:
The inverse gaussian distribution: Some properties and characterizations
Authors: Seshadri V.
Published: June 2006

This article presents some structural properties of the inverse Gaussian distribution, together with several new characterizations based on constancy of regression of suitable functions on the sum ofnindependent identically distributed random variables. A decomposition of the statistic λσ(X−1i−X−1) inton‐ 1 independent chi‐squared random variables, each with one degree of freedom, is given whennis of the form 2r.
Some Bayesian lower bounds on reliability in the lognormal distribution
Authors: Padgett W. J. , Johnson M. P.
Published: June 2006

The two‐parameter lognormal distribution with density function f(y: γ, σ2) = [(2πσ2)1/2y] 1exp[−(ln y − γ)2/2σ2], y > 0, is important as a failure‐time model in life testing. In this paper, Bayesian lower bounds for the reliability function R(t: γ, σ2) = ϕ[(γ − ln t)/σ] are obtained for two cases. First, it is assumed that γ is known and σ2 has either an inverted gamma or “general uniform” prior distribution. Then, for the case that both γ and σ2 are unknown, the normal‐gamma prior and Jeffreys' vague prior are considered. Some Monte Carlo simulations are given to indicate some of the properties of the Bayesian lower bounds.
Multivariate studentization and its applications
Authors: Tan W. Y.
Published: June 2006

In this paper we study the distribution ofT= XS, whereXwith orderp × qis normally distributed with zero expectations and covariance matrix Σ⊗V, (that is,Cov(,) = σij,being thej‐th column ofX, Σ=(σij)) and whereS1′S1=Sis distris uted as Wishart independently ofX, withd.f.=fand parameter matrix Σ=(σij) This is then a multivariate extension of the stu‐dentization process. As we shall see, however, the distribution ofTdepends on howSis partitioned. In this paper we shall consider the cases whereS1is lower triangular with positive diagonal elements and where S, is upper triangular with positive diagonal elements. The distributions ofTcorresponding to these two decompositions ofSare called respectively the upper and lower disguised matrix‐tdistributions. Properties of these distributions are derived. Some applications of these distributions to multivariate regression problems are also pointed out.
Convergence properties of conditional medians
Authors: Tomkins R.J.
Published: June 2006

Certain convergence theorems, akin to results of Lévy and Lebesgue for conditional expectations, are established for conditional medians. An explicit representation of a conditional median is given.
Bayesian nonparametric smoothers for regular processes
Authors: Weerahandi S. , Zidek J. V.
Published: June 2006

This report is about the analysis of stochastic processes of the formR = S + N, whereSis a “smooth” functional andNis noise. The proposed methods derive from the assumption that the observedR‐values and unobserved values ofR, the assumed inferential objectives of the analysis, are linearly related through Taylor series expansions of observed about unobserved values. The expansion errors and all otherprioriunspecified quantities have a joint multivariate normal distribution which expresses the prior uncertainty about their values. The results include interpolators, predictors, and derivative estimates, with credibility‐interval estimates automatically generated in each case. An analysis of an acid‐rain wet‐deposition time series is included to indicate the efficacy of the proposed method. It was this problem which led to the methodological developments reported in this paper.
The one‐way analysis of variance with ordered alternatives: A modification of bartholomew's Ē2Test
Authors: Wright F. T.
Published: June 2006

Tests of homogeneity of normal means with the alternative restricted by an ordering on the means are considered. The simply ordered case, μ1≤ μ2≤ ··· ≤ μk, and the simple tree ordering, μ1≤ μj, for;j= 2, 3,…,k, are emphasized. A modification of the likelihood‐ratio test is proposed which is asymptotically equivalent to it but is more robust to violations of the hypothesized orderings. The new test has power at the points satisfying the hypothesized ordering which is similar to that of the likelihood‐ratio test provided the degrees of freedom are not too small. The modified test is shown to be unbiased and consistent.
Mixed‐scale models for survival/sacrifice experiments
Authors: Rai S. N. , Matthews D. E. , Krewski D. R.
Published: June 2006

Information derived from interim sacrifices or on cause of death is routinely used in the statistical analyses of carcinogenicity experiments involving occult tumours. The authors describe a simple semiparametric model which does not require this information. Natural deaths during the experiment and the usual terminal sacrifice provide sufficient information to ensure that the tumour incidence rates, which are of primary interest in occult‐tumour studies, can be estimated nonparametrically. The advantages of this semiparametric approach to the analysis of survival/sacrifice experiments are illustrated using data from a study on benzyl acetate conducted under the U. S. National Toxicology Program. The results derived compare favourably with those obtained using a previously published approach to the analysis of tumorigenicity data.
Locally best invariant and locally minimax test of independence
Authors: Basu Sujit Kumar , Sinha Bimal Kumar
Published: June 2006

Let X1 X2 … XN be independent normal p‐vectors with common mean vector $$ = ($$) and common nonsingular covariance matrix $$ = Diag ($sGi) [(1–p) I + pE] Diag ($sGi), $sGi> 0, i = 1… p, 1>p>=1/p–1. Write rij = sample correlation between the i th and the j th variable i j = 1,… p. It has been proved that for testing the hypothesis H0 : p = 0 against the alternative H1 : p>0 where $$ and $sG1,…, $sGp are unknown, the test which rejects H0 for large value of $$ rij is locally best invariant for every $aL: 0 > $aL > 1 and locally minimax as p $$ 0 in the sense of Giri and Kiefer, 1964, for every $aL: 0 > $aL $$ $aL0 > 1 where$aL0 = Pp=0 $$.
Designs to guard against outliers in the présence or absence of model bias
Authors: Draper Norman R. , Herzberg Agnes M.
Published: June 2006

Optimality of experimental design is considered in the situation in which individual observations may be subject to a shift in mean. The criterion of minimum average integrated mean square error is examined in general and the consequences for first and second degree models in the présence or absence of model bias are discussed.
A comparison of alternative rate estimators in some frequently used growth models
Authors: Ramasubban T. A.
Published: June 2006

This paper deals with the linear, exponential and Gompertz models and compares the bias and variance of a number of estimators of the growth‐rate parameters of these models. Some of these estimators have been commonly recommended in the literature and others are most frequently used in empirical practice. The present analysis points to the strengths and weaknesses of the estimators in their usage.
Stochastic models of failure in random environments
Authors: Desmond Anthony
Published: June 2006

Stochastic models of failure modes of frequent occurrence in the engineering sciences are considered. The failure‐producing stress environment is modelled as a stationary stochastic process. Using theoretical properties of the sample paths of these processes, failure‐time distributions which belong to the Birnbaum‐Saunders family are obtained. Several examples of particular engineering relevance are treated.
Regression analysis and ratio analysis for domains: A randomization‐theory approach
Authors: Elvers Eva , SÄRNDAL Carl Erik , Wretman Jan H. , ÖRNBERG Göran
Published: June 2006

In most surveys, inference for domains poses a difficult problem because of data shortage. This paper presents a probability sampling theory approach to some common types of statistical analysis for domains of a surveyed population. Simple and multiple regression analysis, and analysis of ratios are considered. Two new methods are constructed and explored which can improve substantially over the common method based on sample‐weighted sums of squares and products. These new methods use auxiliary variables whose importance depends on the extent to which they succeed in explaining certain patterns in the regression residuals. The theoretical conclusions are supported by empirical results from Monte Carlo experiments.
Approach to normality of mean and M‐estimators of location
Authors: Field Christopher
Published: June 2006

The approach to normality of an estimate is displayed graphically by the nonlinearity in the derivative of the log density, and this nonlinearity is related to the accuracy of the normal approximation for the tail area. Using techniques from small‐sample asymptotics, an alternate proof of the central limit theorem is given and same indices of tail behavior are examined.
On the asymptotic efficiency of aligned‐rank tests in randomized block designs
Authors: Tardif Serge
Published: June 2006

This paper is concerned with the ranking‐after‐alignment procedure, the alignment being made on the mean, in randomized block designs. The asymptotic efficiencies, as the number of blocks goes to infinity, of a class of aligned‐rank tests, relative to the maximin most powerful test based on aligned observations, are established and studied. Some asymptotic efficiencies under doubleexponentiality are also obtained using Monte Carlo methods.
The asymptotic distribution of the correlation coefficient in testing fit to the exponential distribution
Authors: Lockhart R. A.
Published: June 2006

The asymptotic distribution of certain tests of fit to the exponential distribution is obtained. The tests are based on regression of the order statistics on their expectations under a standard exponential distribution. Asymptotic normality at the rate (logn)1/2is obtained for a family of statistics including the correlation coefficient.
Goodness‐of‐link testing in ordinal regression models
Authors: Genter Frederic C. , Farewell Vernon T.
Published: June 2006

McCullagh (1980) presented a comprehensive review of regression models for ordinal response variables. In these models, the functional relationship between the covariates and the response categories is dependent on thelink function. This paper shows that discrimination between links is feasible when the response variable is ordinal. Using the log‐gamma distribution of Prentice (1974), a generalized link function is constructed which allows discrimination between the probit, log‐log, and complementary log‐log links. Sample‐size considerations are noted, and examples are presented.
Comparison of two life distributions on the basis of their percentile residual life functions
Authors: Joe Harry , Proschan Frank
Published: June 2006

LetFandGbe life distributions with respective failure rate functionsrFandrGand respective 100α‐percentile (0 < α < 1) residual life functionsqα,F, andqα, G. Distribution‐free two‐sample tests are proposed for testingH0:F=GagainstH1,α,:qα,F≥qα,GandH2 α:qβ,F≥qβ,Gfor all β ≥ α. This class of tests includes as a special case the test of Kochar (1981) for the alternativeH*2:rF≤rG. A theorem of Govindarajulu (1976) is extended in order to obtain asymptotic normality of the test statistics. The conditionqα,F≥qα,Gis implied byrF≤rGand is unrelated to the stochastic orderingF≤G; ifFandGare Weibull distributions with respective shape parametersc1andc2such that 1 ≤C1<C2, thenqα,F≥qα,Gfor all α larger than a function of the parameters.
Relative efficiencies of goodness‐of‐fit procedures with truncated data
Authors: Koziol James A. , John Petkau A.
Published: June 2006

Efficiency properties of the Kolmogorov‐Smirnov, Kuiper, Cramér‐von Mises, and Anderson‐Darling statistics with truncated data are investigated. For these statistics, the approximate slopes are determined, and the equivalence of ratios of limiting approximate slopes to limiting Pitman efficiencies is established. Efficiencies for certain parametric families of distributions incorporating both location and scale alternatives are evaluated as the amount of truncation increases.
On the distribution of the correlation coefficient when sampling from a mixture of two bivariate normal densities: Robustness and the effect of outliers
Authors: Srivastava M. S. , Lee G. C.
Published: June 2006

The distribution of the sample correlation coefficient is derived when the population is a mixture of two bivariate normal distributions with zero mean but different covariances and mixing proportions 1 ‐ λ and λ respectively; λ will be called the proportion of contamination. The test of ρ = 0 based on Student'st, Fisher'sz, arcsine, or Ruben's transformation is shown numerically to be nonrobust when λ, the proportion of contamination, lies between 0.05 and 0.50 and the contaminated population has 9 times the variance of the standard (bivariate normal) population. These tests are also sensitive to the presence of outliers.
A reexamination of stein's antifiducial example
Authors: Plante AndrÉ
Published: June 2006

In Stein's 1959 example, for any sample withnsufficiently large, there is a confidence set embedded simultaneously within two regular confidence belts—one with coverage frequency smaller than an arbitrary positive ϵ, the other with coverage frequency larger than 1 — ϵ. Thus, Stein's example may be seen as an extreme case of mutually conflicting confidence statements, illustrating a possibility anticipated and denounced by Fisher.
A note on the construction of some lattices for the hypercubic association scheme
Authors: Duthie Audrey I.
Published: June 2006

This paper presents a method of construction for some PBIB lattices for the hypercubic association scheme.
Bayesian nonparametric survival analysis for grouped data
Authors: Johnson Wesley , Christensen Ronald
Published: June 2006

A Bayesian nonparametric estimate of the survival distribution is derived under a particular sampling scheme for grouped data that includes the possibility of censoring. The estimate uses the prior information to smooth the data, giving an estimate which is continuous. As special cases survival estimates for life tables are obtained and the estimate of Susarla and Van Ryzin (1976) is derived. As the weight of the prior information tends to zero, the Bayesian estimate reduces to a continuous version of the nonparametric maximum‐likelihood estimate. An empirical Bayes modification of the procedure is illustrated on a data set from Cutler and Ederer (1958).
Optimal confidence regions in GMANOVA
Authors: Hooper Peter M. , Yau Wai Kwok
Published: June 2006

Invariant confidence regions with smallest expected normalized volume are derived for a matrix of means of interest in the GMANOVA model, assuming only that the distribution of the matrix of residuals is left orthogonally invariant. Two invariance groups are considered, the usual full group and an amenable subgroup. A particular choice of the normalizing term leads to conditionally optimal confidence regions. Numerical results are given comparing the conditionally optimal fully invariant confidence region, which corresponds to the likelihood‐ratio test, with a conditionally minimax confidence region.
Censoring, conditionally, and likelihood
Authors: Wasserman Larry A.
Published: June 2006

The censoring principle is shown to imply a principle similar to the likelihood principle. Further, it is demonstrated that the censoring principle and a weak form of the conditionality principle jointly imply the likelihood principle.
Approximate theory of multiway block designs
Authors: Pukelsheim Friedrich
Published: June 2006

Optimality properties of multiway block designs are deduced from the general results of J. Kiefer's approximate‐design theory. In the model with additive effects these optimality properties solely depend on the two‐dimensional marginals of the designs. Uniform designs, and designs whose two‐dimensional marginals are products of the one‐dimensional marginals, are shown to be optimal. Approximate Youden designs are introduced for the case when the support sets of the two‐dimensional marginals are prescribed in advance. They are optimal in a relatively small class of competing designs only.
Approximations to noncentral distributions
Authors: Cox David R. , Reid Nancy
Published: June 2006

Two methods for approximating the distribution of a noncentral random variable by a central distribution in the same family are presented. The first consists of relating a stochastic expansion of a random variable to a corresponding asymptotic expansion for its distribution function. The second approximates the cumulant generating function and is used to provide central χ2and gamma approximations to the noncentral χ2and gamma distributions.
Residual components in generalized linear models
Authors: Brant Rollin
Published: June 2006

The adequacy of a postulated generalized linear model can often be improved by transforming predictors and/or including additional explanatory variables. To assess the fit relative to a given predictor, we define its corresponding residual component. Asymptotic bias and variance of the residual component are considered, paying particular attention to the case that the presumed model is valid.
Conditional and predictive probability integral transforms
Authors: O'Reilly Federico J. , Villegas Cesareo
Published: June 2006

The conditional probability integral transform, used in goodness‐of‐fit tests, is compared with its Bayesian counterpart, the predictive probability integral transform, and it is shown that under suitable conditions, in the presence of an adequate group structure, they yield the same transformed random variable, usually uniform on the unit interval.
Equivariant estimation of a normal mean using a normal concomitant variable for covariance adjustment
Authors: Berry J. Calvin
Published: June 2006

Equivariant point estimators of one component of a bivariate normal mean vector are considered when the second component is known. Equivariant point estimators are characterized and compared in terms of their risk functions with respect to a normalized squared‐error loss function. Specific point estimators that dominate the usual estimator when the squared correlation coefficient is sufficiently large are provided.
Use of time‐series methods in the preparation of quarterly estimates of vital events
Authors: Roberts Georgia R.
Published: June 2006

This paper considers the problem of producing quarterly estimates of provincial and national vital events. Modern time‐series methods would appear to be a promising tool for the short‐range forecasts required for the birth, death, and marriage series. Considerations in the choice of a suitable model are described, and a possible model for the marriage data is illustrated.
Likelihood
Authors: Hinkley David V.
Published: June 2006

This article reviews some recent work on large‐sample likelihood inference, in particular work related to conditional inference and ancillary statistics. The background discussion includes a relation between conditional inference and testing for model fit. There are brief comments on results for sequential estimation, also on the difficulties associated with multiparameter problems.
The function space D([O, ∞)ρ, E)
Authors: Ivanoff B. Gail
Published: June 2006

The Skorokhod topology is extended to the function spaceD([0, ∞)ρ,E) of functions, from [0, ∞)ρ to a complete separable metric spaceE, which are “continuous from above with limits from below. Criteria for tightness are developed. The case in whichEis a product space is considered, and conditions under which tightness may be proven componentwise are given. Various applications are studied, including a multidimensional version of Donsker's Theorem, and a functional Central Limit Theorem for a multitype Poisson cluster process.
A new test for residual randomness in a class of dynamic autocorrelated econometric models
Authors: Kerward L. R.
Published: June 2006

This paper presents a new test statistic for dynamic or stochastic mis‐specification for the dynamic demand or dynamic adjustment class of economic models. The test statistic is based on residual autocorrelations, asymptotically X2and is suspected to be of low power. The test is illustrated with an example from recent econometric literature.
Estimation bayesienne des effets dans le modele a effets aleatoires de classification double avec interaction
Authors: Clement Bernard
Published: June 2006

The problem of estimating the effects in a balanced two‐way classification with interaction

\documentclass{article}\pagestyle{empty}\begin{document}$i = 1, \ldots ,I;j = 1, \ldots ,J;k = 1, \ldots ,K$\end{document}using a random effect model is considered from a Bayesian view point. Posterior distributions ofri,cjandtijare obtained under the assumptions thatri,cj,tijandeijkare all independently drawn from normal distributions with zero meansand variances\documentclass{article}\pagestyle{empty}\begin{document}$\sigma _r^2 ,\sigma _c^2 ,\sigma _t^2 ,\sigma _e^2$\end{document}respectively. A non informative reference prior is adopted for\documentclass{article}\pagestyle{empty}\begin{document}$\mu ,\sigma _r^2 ,\sigma _c^2 ,\sigma _t^2 ,\sigma _e^2$\end{document}. Various features of thisposterior distribution are obtained. The same features of the psoterior distribution for a fixed effect model are also obtained. A numerical example is given.
Some computational problems related to multinomial trials
Authors: Neuts Marcel F. , Carson Charles C.
Published: June 2006

Efficient numerical algorithms are developed to evaluate several probabilities related to multinomial trials.In the first part of the paper, the probability distribution of the number of trials until the alternatives j, j = 1,… m, have occurred at least ij times is computed. The multinomial trials involve the m alternatives l,…, m, with positive probabilities Pl‐Pm of occurrence.

In the second part, several aspects of a multinomial subset selection problem, discussed by S. S. Gupta and K. Nagel, are investigated.
Estimation of the mean utilizing prior information
Authors: Mehta J. S. , Raghunandanan K.
Published: June 2006

Katti [1] et Mehta et Srinivasan [2] ont considérés le probléme d'estimer la moyenne μ d'une population quand de l'information a priori sur μ est disponible. Dans [1], la supposition est que cette information a priori est sous forme d'un “estimé deviné”. Un estimateur à deux degres de deux échantillons est présenté. Quand à [2], un estimateur “shrinkage” basé sur un seul échantillon et une “valeur à priori” est considéré. En suivant les techniques présentées dans ces deux articles, nous suggérons des estimateurs du paramètre quand les données viennent d'une population Binomiale ou Poisson.
Excursion and meander in random walk
Authors: Csáki E. , Mohanty S. G.
Published: June 2006

Bernoulli bridge, excursion and meander are defined on the symmetric random walk similarly to Brownian bridge, excursion and meander (cf. Chung 1976). Distributions of certain characteristics defined on these Bernoulli processes, which are of a combinatorial nature, and their limits are obtained. Using weak convergence, these derivations give a verification of some of the earlier results on Brownian excursion and Brownian meander, as well as some new results.
Asymptotic properties of randomly indexed sequences of random variables
Authors: Csörgó M. , Rychlik Z.
Published: June 2006

Conditions are given for a randomly indexed sequence of random variables to converge weakly. The key concept employed is the so‐called generalized Anscombe condition. The results give a method of determining sequential stopping rules, which have the required accuracy of estimation of an unknown parameter in the case when the observations are not necessarily independent and identically distributed.
Factor analysis regression
Authors: Basilevsky Alexander
Published: June 2006

The paper describes two regression models—principal components and maximum‐likelihood factor analysis—which may be used when the stochastic predictor varibles are highly intereorrelated and/or contain measurement error. The two problems can occur jointly, for example in social‐survey data where the true (but unobserved) covariance matrix can be singular. Departure from singularity of the sample dispersion matrix is then due to measurement error. We first consider the more elementary principal components regression model, where it is shown that it can be derived as a special case of (i) canonical correlation, and (ii) restricted least squares. The second part consists of the more general maximum‐likelihood factor‐analysis regression model, which is derived from the generalized inverse of the product of two singular matrices. Also, it is proved that factor‐analysis regression can be considered as an instrumental variables estimator and therefore does not depend on whether factors have been “properly” identified in terms of substantive behaviour. Consequently the additional task of rotating factors to “simple structure” does not arise.
A robust biplot
Authors: Daigle Gaétan , Rivest Louis‐Paul
Published: June 2006

This paper introduces a robust biplot which is related to multivariateM‐estimates. Then × pdata matrix is first considered as a sample of sizenfrom somep‐variate population, and robustM‐estimates of the population location vector and scatter matrix are calculated. In the construction of the biplot, each row of the data matrix is assigned a weight determined in the preliminary robust estimation. In a robust biplot, one can plot the variables in order to represent characteristics of the robust variance‐covariance matrix: the length of the vector representing a variable is proportional to its robust standard deviation, while the cosine of the angle between two variables is approximately equal to their robust correlation. The proposed biplot also permits a meaningful representation of the variables in a robust principal‐component analysis. The discrepancies between least‐squares and robust biplots are illustrated in an example.
A general method of finding a minimax estimator of a distribution function when no equalizer rule is available
Authors: Yu Qiqing
Published: June 2006

We propose a feasible general method for finding a minimax estimator of an unknown distribution function F in the nonparametric problem. As an application, some minimax estimators are proposed. Furthermore, some minimax binomial parametric problems are studied.
A zero‐one law for large order statistics
Authors: Wang H. , Tomkins R. J.
Published: June 2006

Fix r ≥ 1, and let {Mnr} be the rth largest of {X1,X2,…Xn}, where X1,X2,… is a sequence of i.i.d. random variables with distribution function F. It is proved that P[Mnr ≤ un i.o.] = 0 or 1 according as the series Σ∞n=3Fn(un)(log log n)r/n converges or diverges, for any real sequence {un} such that n{1 ‐F(un)} is nondecreasing and divergent. This generalizes a result of Bamdorff‐Nielsen (1961) in the case r = 1.
Approximation spline de la prevision d'un processus fonctionnel autorégressif d'ordre 1
Authors: Besse Philippe C. , Cardot Hervé
Published: June 2006

ABSTRACT We present a method to approximate and forecast, on an entire interval, a continuous‐time process. For this purpose, we use the modelization of ARH(l) processes, defined by Bosq (1991). We deal with the practical problem of the discretization of the observed trajectories and approximate them by means of spline functions. We show by simulations that for well‐chosen smoothing parameters, good prediction can be obtained in comparison with the “predictable” part of the process. Finally, we apply this model to forecast road traffic and compare it with a SARIMA model.
Distribution of the cross‐correlations of squared residuals in ARIMA models
Authors: Wong H. , Li W. K.
Published: June 2006

ABSTRACT The distribution of the cross‐correlations of squared residuals from Box‐Jenkins models is considered in very general conditions, and the asymptotic distribution is derived. A test for a lagged relationship in volatility for economic time series under instantaneous causality is proposed, and its empirical behaviour is studied. An example involving the international stock market's volatility is studied, and an interesting result is observed.
Model influence functions based on mixtures
Authors: Gustafson Paul
Published: June 2006

Influence functions are considered as diagnostics for model departures in parametric Bayesian inference. A baseline model density is expressed as a mixture; then the mixing distribution is perturbed. This is designed to engender perturbations which are plausiblea priori.The influence of perturbations is measured for both Bayes estimates and their associated posterior expected losses. To assess the plausibility of perturbationsa posteriori, an additional influence function is constructed for the Bayes factor comparing the perturbed and baseline models. The effect of perturbation on various estimands is incorporated in the analysis.
Nonparametric regression estimation at design poles and zeros
Authors: Hengartner Nicolas W. , Linton Oliver B.
Published: June 2006

ABSTRACT In most treatments of nonparametric regression, it is assumed that the marginal density of the explanatory variables is strictly bounded away from zero and infinity. This note investigates the pointwise asymptotics for nonparametric regression when this assumption fails, that is, the marginal density of the explanatory variable has either an isolated zero or a pole at the point of interest.
Bayesian semiparametric inference for the accelerated failure‐time model
Authors: Kuo Lynn , Mallick Bani
Published: June 2006

Bayesian semiparametric inference is considered for a loglinear model. This model consists of a parametric component for the regression coefficients and a nonparametric component for the unknown error distribution. Bayesian analysis is studied for the case of a parametric prior on the regression coefficients and a mixture‐of‐Dirichlet‐processes prior on the unknown error distribution. A Markov‐chain Monte Carlo (MCMC) method is developed to compute the features of the posterior distribution. A model selection method for obtaining a more parsimonious set of predictors is studied. The method adds indicator variables to the regression equation. The set of indicator variables represents all the possible subsets to be considered. A MCMC method is developed to search stochastically for the best subset. These procedures are applied to two examples, one with censored data.
Line transects of two‐dimensional random fields: Estimation and design
Authors: Heckman Nancy , Rice John
Published: June 2006

In line‐transect sampling data are collected continuously along the path travelled. These data are then used to estimate some characteristic of an entire region. We model the characteristic of the region as a linear functional ofZ(), a realization of a random field, and our data as the values ofZ(x) for x along the path. We study how to estimate the characteristic of interest and how to choose the path to accurately estimate it.
Applications of bivariate and univariate local lyapunov exponents
Authors: Seifu Yodit , Reid N.
Published: June 2006

Chaotic systems are characterized by sensitivity to initial conditions, and this property can be measured by global Lyapunov exponents, which are measures of the average divergence rate of initially close trajectories. Wolff (1992) introduced local Lyapunov exponents and used them to obtain two diagnostic plots for differentiating between stochastic and deterministic time series. We extend the definition of the local Lyapunov exponent and the diagnostic plots to accommodate time series that arise from bivariate maps and investigate the behaviour of the local Lyapunov exponents and the corresponding diagnostic plots for some dynamical systems and stochastic time series. We consider the application of these diagnostic plots to some heart rate variability data.
Dataset on silver‐maple‐tree growth regulators
Authors: Sloan Jef F. A. , Schwarz Carl J. , Neden Linda R.
Published: June 2006

A trivariate summary measure based upon the number of sprouts, the lengths of the sprouts, and the number of intemodes per sprout was developed to compare the effects of growth suppressants on tree regrowth after trimming. A new graphic, the tree picture, was developed to display this information. The tree picture is easy to interpret and revealed clear results for the data given. These results demonstrate how innovative graphical methodology can be applied as a summary device in the absence of or as a supplement to a statistical testing procedure.
Conditional inference for subject‐specific and marginal agreement: Two families of agreement measures
Authors: Cook Richard J. , Farewell Vern T.
Published: June 2006

A two‐stage procedure is described for assessing subject‐specific and marginal agreement for data from a test‐retest reliability study of a binary classification procedure. Subject‐specific agreement is parametrized through the log odds ratio, while marginal agreement is reflected by the log ratio of the off‐diagonal Poisson means. A family of agreement measures in the interval [‐1, 1] is presented for both types of agreement. The conditioning argument described facilitates exact inference. The proposed methodology is demonstrated by way of an example involving hypothetical data chosen for illustrative purposes, and data from a National Health Survey Study (Rogot and Goldberg 1966).
Nonparametric function estimation from inversely sampled record‐breaking data
Authors: Gulati Sneh , Padgett W. J.
Published: June 2006

Often, in industrial stress testing, meteorological data analysis, and other similar situations, measurements may be made sequentially and only values smaller than all previous ones are recorded. When the number of records is fixed in advance, the data are referred to as inversely sampled record‐breaking data. This paper is concerned with nonparametric estimation of the distribution and density functions from such data (successive minima). For a single record‐breaking sample, consistent estimation is not possible except in the extreme left tail of the distribution. Hence, replication is required, and formsuch independent record‐breaking samples, the estimators are shown to be strongly consistent and asymptotically normal asm∞ →. Computer simulations are used to investigate the effect of the bandwidth on the mean squared errors and biases of the smooth estimators, and are also used to provide a comparison of their performance with the analogous estimators obtained under random sampling for record values.
Asymptotic distribution of data‐driven smoothers in density and regression estimation under dependence
Authors: Boente Graciela , Fraiman Ricardo
Published: June 2006

We consider automatic data‐driven density, regression and autoregression estimates, based on any random bandwidth selector h/T. We show that in a first‐order asymptotic approximation they behave as well as the related estimates obtained with the “optimal” bandwidthhTas long ashT/hT→ 1 in probability. The results are obtained for dependent observations; some of them are also new for independent observations.
Generalized Laplacian approximations in Bayesian inference
Authors: HSU John S. J.
Published: June 2006

This paper presents a new Laplacian approximation to the posterior density of η = g(θ). It has a simpler analytical form than that described by Leonard et al. (1989). The approximation derived by Leonard et al. requires a conditional information matrix Rη to be positive definite for every fixed η. However, in many cases, not all Rη are positive definite. In such cases, the computations of their approximations fail, since the approximation cannot be normalized. However, the new approximation may be modified so that the corresponding conditional information matrix can be made positive definite for every fixed η. In addition, a Bayesian procedure for contingency‐table model checking is provided. An example of cross‐classification between the educational level of a wife and fertility‐planning status of couples is used for explanation. Various Laplacian approximations are computed and compared in this example and in an example of public school expenditures in the context of Bayesian analysis of the multiparameter Fisher‐Behrens problem.
Uniqueness of the least‐distances estimator in regression models with multivariate response
Authors: Ducharme Gilles R.
Published: June 2006

In a regression model with univariate response, the quantities derived from the least‐absolute‐deviations method need not be unique. In this note, we show that, contrary to the univariate case, in a regression model with multivariate response, the least‐distances method typically yields quantities that exhibit uniqueness properties that are similar to those obtained by the least‐squares method.
Uniform validity of saddlepoint expansion on compact sets
Authors: Routledge Rick , Tsao Min
Published: June 2006

This paper shows that Daniels's (1954) saddlepoint expansion for the density of a sample mean is, for all practical purposes, always uniformly valid on compact subsets in the interior of the domain of the mean. This uniform validity is the key for establishing the relation between the saddlepoint expansion for the density function and Lugannani and Rice's expansion for the tail probability, and for establishing the validity of a high‐order asymptotic expansion for the density of a standardized mean.
Asymptotic normality for chi‐bar‐square distributions
Authors: Dykstra Richard
Published: June 2006

Chi‐bar‐square distributions, which are mixtures of chi‐square distributions, mixed over their degrees of freedom, often occur when testing hypotheses that involve inequality constraints. Here, necessary and sufficient conditions on the mixing or weighting distribution are found to ensure asymptotic normality of the corresponding chi‐bar‐square distribution. Essentially, asymptotic normality occurs for the chi‐bar‐square distribution if either the ratio of the mean to the variance of the mixing distribution goes to infinity, or the weighting distribution itself is asymptotically normal. Other than a combination of these two phenomena, this is also the only way for asymptotic normality to hold. Several examples of pertinent chi‐bar‐square distributions are shown to be asymptotically normal by the results in this paper.
Multiple‐shrinkage estimators of means in exponential families
Authors: And Fanny Ki , Tsui Kam‐Wah
Published: June 2006

Shrinkage estimators are often obtained by adjusting the usual estimator towards a target subspace to which the true parameter might belong. However, meaningful reductions in risk below the usual estimator can typically be achieved in a very small part of the parameter space. In the multivariate‐normal mean estimation problem, E. George, in a series of papers, showed how multiple‐shrinkage estimators (data‐weighted averages of several different shrinkage estimators) can attain substantial risk reductions in a large part of the parameter space. This paper extends the multiple‐shrinkage results to the case of simultaneous estimation of the means of several one‐parameter exponential families. Our results are developed by using an identity similar to that of Haff and Johnson (1986). A computer simulation is reported to indicate the magnitude of reductions in risk. Our results are also applied to the problem of how to choose appropriate component variables to combine before a suitable shrinkage estimator is considered.
The power of the circular cone test: A noncentral chi‐bar‐squared distribution
Authors: Conaway Mark , Pillers Carolyn , Robertson Tim , Sconing James
Published: June 2006

Pincus (1975) derived the null distribution of the likelihood‐ratio test statistic for testing that the mean vector of a multivariate normal distribution is zero against the alternative that the mean vector lies in a circular cone. Under the null hypothesis, the likelihood‐ratio test statistic has a chi‐bar‐squared distribution. We extend the results of Pincus by deriving the distribution of the likelihood‐ratio test statistic under the alternative hypothesis. In a special case, the distribution is a “noncentral chi‐bar‐squared” distribution. To our knowledge, this is the first order‐restricted testing problem for which the relationship between the null and alternative distributions of the test statistic is similar to the relationship in the linear‐model setting. That is, the distribution of the likelihood‐ratio test has a central form of a distribution under the null hypothesis and a noncentral form of the same distribution under the alternative.
Asymptotic behaviour of nonparametric conditional quantile estimates for time series
Authors: Shi Peide
Published: June 2006

Nonparametric regression quantiles provide informative and powerful alternatives and generalizations to the more traditional mean and median. The use of B‐spline approximation in the conditional quantile estimation has been studied recently by He and Shi (1994). The regression quantile splines are given by minimizing n i = 1 ρα(Yi‐ g(Xi))where ρα(t) = |t| ‐ (2α ‐ 1)t is the Czech function and g is taken from the space spanned by normalized B‐splines basis functions. This paper relaxes the independence assumption on the stationary sequence {Xi, Yi}. If the true conditional quantile function is smooth up to order r and the observed sequence is β‐mixing (or absolutely regular), it is shown, under suitable mixing conditions, that the optimal global convergence rates can be achieved by the B‐spline based estimators and their derivatives.

Les fractiles de régression non‐paramétriques donnent d'éclairantes et puissantes alternatives et généralisations aux traditionelles moyenne et médiane. L'utilisation d'approximations par B‐splines dans l'estimation conditionnelle du fractile a été étudiée récemment par He et Shi (1994). Les splines des fractiles de régression sont obtenus en minimisant n i = 1 ρα(Yi‐ g(Xi)), o ù ρα(t) = |t| ‐ (2α ‐ 1)t est la fonction de Czech et g est pris dans l'espace généré par une base de fonctions composé de B‐splines normalisées. Cet article affaiblit l'hypothèse d'indépendance de la suite stationnaire {Xi, Yi,}. Si la véritable fonction fractile est lisse d'ordre r et la suite observée est β‐mixante (ou absolument régulière), il est montré, sous des hypothèses appropriées de mixage, que les taux obtimaux de convergence global peuvent ětre obtenus par des estimateurs basés sur les B‐splines et leurs dérivés.
Approximations for marginal densities of M‐estimators
Authors: Fan Rocky Y.K. , Field Christopher A.
Published: June 2006

We develop a saddle‐point approximation for the marginal density of a real‐valued function p(), where is a general M‐estimator of a p‐dimensional parameter, that is, the solution of the system {n‐1ljl(Yl,) = 0}j=1,…,p. The approximation is applied to several regression problems and yields very good accuracy for small samples. This enables us to compare different classes of estimators according to their finite‐sample properties and to determine when asymptotic approximations are useful in practice.
Bayesian analysis of outlier problems using divergence measures
Authors: Peng Fengchun , Dey Dipak K.
Published: June 2006

A Bayesian approach is presented for detecting influential observations using general divergence measures on the posterior distributions. A sampling‐based approach using a Gibbs or Metropolis‐within‐Gibbs method is used to compute the posterior divergence measures. Four specific measures are proposed, which convey the effects of a single observation or covariate on the posterior. The technique is applied to a generalized linear model with binary response data, an overdispersed model and a nonlinear model. An asymptotic approximation using Laplace method to obtain the posterior divergence is also briefly discussed.
A necessary and sufficient condition for the strong consistency of a family of estimators of the common odds ratio
Authors: Yu Kai Fun
Published: June 2006

A family of easily computable estimators of the odds ratio of a number of two‐by‐two contingency tables is proposed. It includes the well‐known Mantel‐Haenszel estimator as a special case. A necessary and sufficient condition is given for the strong consistency of the estimators for the case when the tables are sparse and the number of tables becomes large. The condition also ensures the asymptotic normality of this family of estimators. A family of consistent estimators is proposed for the variances of the asymptotic distributions. In the case of the Mantel‐Haenszel estimator, the validity of Breslow's (1981, Biometrika) condition for the consistency and asymptotic normality is questioned. Examples are given to demonstrate that it is neither necessary nor sufficient for the consistency of the Mantel‐Haenszel estimator.

Cet article propose une famille d'estimateurs faciles à calculer du rapport‐chance d'un certain nombre de tableaux de contingences deux par deux. Elle comprend le fameux estimateur de Mantel‐Haenszel, comme cas particulier. Une condition nécessaire et suffisante pour la convergence forte des estimateurs est donnée, dans le cas où les tableaux sont clairsemés et le nombre de tableaux devient élevé. Cette condition garantit également la normalité asymptotique de cette famille d'estimateurs. Une famille d'estimateurs convergents est proposée pour les variances des distributions aymptotiques. Dans le cas de l'estimateur de Mantel‐Haenszel, la validité de la condition de Breslow (1981, Biometrika) pour la convergence et la normalité asymptotique est remise en cause. Des examples sont fournis, démontrant qu'elle n'est ni nécessaire ni suffisante pour la convergence de l'estimateur de Mantel‐Haenszel.
Belief functions and statistical inference
Authors: Wasserman Larry A.
Published: June 2006

The Dempster Shafer theory of belief functions is a method of quantifying uncertainty that generalizes probability theory. We review the theory of belief functions in the context of statistical inference. We mainly focus on a particular belief function based on the likelihood function and its application to problems with partial prior information. We also consider connections to upper and lower probabilities and Bayesian robustness.
Gaussian‐based kernels
Authors: Wand Matthew P. , Schucany William R.
Published: June 2006

We derive a class of higher‐order kernels for estimation of densities and their derivatives, which can be viewed as an extension of the second‐order Gaussian kernel. These kernels have some attractive properties such as smoothness, manageable convolution formulae, and Fourier transforms. One important application is the higher‐order extension of exact calculations of the mean integrated squared error. The proposed kernels also have the advantage of simplifying computations of common window‐width selection algorithms such as least‐squares cross‐validation. Efficiency calculations indicate that the Gaussian‐based kernels perform almost as well as the optimal polynomial kernels when die order of the derivative being estimated is low.
Saddlepoint approximations for nonlinear statistics
Authors: Wang Soujin
Published: June 2006

It is well known that saddlepoint expansions lead to accurate approximations to the cumulative distributions and densities of a sample mean and other simple linear statistics. The use of such expansions is explored in a broader situation. The saddlepoint formula for the tail probability of a certain type of nonlinear statistic is derived. The relative error ofO(n–1), as in the linear case, is retained. A simple example is considered, to illustrate the great accuracy of the approximation.