bluuebunny/crossref_metadata_2025 huggingface dataset:
Test de différence de contrastes et somme pondérée de khi‐deux
Authors: Bayomog Samuel , Guyon Xavier , Hardouin Cécile , Yao Jianfeng
Published: June 2006

After recalling the framework of minimum‐contrast estimation, its consistency and its asymptotic normality, we highlight the fact that these results do not require any stationarity or ergodicity assumptions. The asymptotic distribution of the underlying contrast difference test is a weighted sum of independent chi‐square variables having one degree of freedom each. We illustrate these results in three contexts: (1) a nonhomogeneous Markov chain with likelihood contrast; (2) a Markov field with coding, pseudolikelihood or likelihood contrasts; (3) a not necessarily Gaussian time series with Whittle's contrast. In contexts (2) and (3), we compare experimentally the power of the likelihood‐ratio test with those of other contrast‐difference tests.
Concepts and measures for skewness with data‐analytic implications
Authors: Benjamini Yoav , Krieger Abba M.
Published: June 2006

The decomposition of the distribution function into skewness and spread functions serves as a basis for conceptualizing the skewness of a random variable. Measures of skewness are also described in terms of the skewness and spread functions, thereby unifying the measures with the concepts. Results that relate these measures to whether one random variable is more skewed than another are reviewed and extended. Graphical displays are presented for uncovering the nature of the skewness of a variable. The measures are also linked to the issue of symmetrizing a variable.
La médiane simpliciale d'Oja: Existence, unicité et stabilité
Authors: LeÓan Carlos Antonio , Massé Jean‐Claude
Published: June 2006

Oja (1983) examined various ways of measuring location, scatter, skewness, and kurtosis for multivariate distributions. Among other measures of location, he introduced a generalised median known in this paper under the name of the Oja median. In our study of the existence of that median, we show that Oja's definition can only be applied to distributions having a mean. In dimension d θ 2, we establish that the usual method of extension breaks down, which raises the question of the validity of the concept as a notion of median. Two fundamental theoretical properties of that median are also considered: uniqueness and consistency.
Generalized additive models for longitudinal data
Authors: Berhane Kiros , Tibshirani Robert J.
Published: June 2006

We introduce a class of models for longitudinal data by extending the generalized estimating equations approach of Liang and Zeger (1986) to incorporate the flexibility of nonparametric smoothing. The algorithm provides a unified estimation procedure for marginal distributions from the exponential family. We propose pointwise standard‐error bands and approximate likelihood‐ratio and score tests for inference. The algorithm is formally derived by using the penalized quasilikelihood framework. Convergence of the estimating equations and consistency of the resulting solutions are discussed. We illustrate the algorithm with data on the population dynamics of Colorado potato beetles on potato plants.
A stochastic approximation algorithm for maximum‐likelihood estimation with incomplete data
Authors: Gu Ming Gao , Li Shaolin
Published: June 2006

We propose a new stochastic approximation (SA) algorithm for maximum‐likelihood estimation (MLE) in the incomplete‐data setting. This algorithm is most useful for problems when the EM algorithm is not possible due to an intractable E‐step or M‐step. Compared to other algorithm that have been proposed for intractable EM problems, such as the MCEM algorithm of Wei and Tanner (1990), our proposed algorithm appears more generally applicable and efficient. The approach we adopt is inspired by the Robbins‐Monro (1951) stochastic approximation procedure, and we show that the proposed algorithm can be used to solve some of the long‐standing problems in computing an MLE with incomplete data. We prove that in generalO(n) simulation steps are required in computing the MLE with the SA algorithm andO(nlogn) simulation steps are required in computing the MLE using the MCEM and/or the MCNR algorithm, wherenis the sample size of the observations. Examples include computing the MLE in the nonlinear error‐in‐variable model and nonlinear regression model with random effects.
Asymptotic properties of the GMLE in the case 1 interval‐censorship model with discrete inspection times
Authors: Yu Qiqing , Schick Anton , Li Linxiong , Wong George Y. C.
Published: June 2006

We consider the case 1 interval censorship model in which the survival time has an arbitrary distribution functionF0and the inspection time has a discrete distribution functionG. In such a model one is only able to observe the inspection time and whether the value of the survival time lies before or after the inspection time. We prove the strong consistency of the generalized maximum‐likelihood estimate (GMLE) of the distribution functionF0at the support points ofGand its asymptotic normality and efficiency at what we call regular points. We also present a consistent estimate of the asymptotic variance at these points. The first result implies uniform strong consistency on [0, ∞) ifF0is continuous and the support ofGis dense in [0, ∞). For arbitraryF0andG, Peto (1973) and Tumbull (1976) conjectured that the convergence for the GMLE is at the usual parametric raten½ Our asymptotic normality result supports their conjecture under our assumptions. But their conjecture was disproved by Groeneboom and Wellner (1992), who obtained the nonparametric rate ni under smoothness assumptions on theF0andG.
Pseudolikelihood estimation in a class of problems with response‐related missing covariates
Authors: Joan HU X. , Lawless Jerald F.
Published: June 2006

Many practical situations involve a response variableYand covariatesX, where data on (Y,X) are incomplete for some portion of a sample of individuals. We consider two general types of pseudolikelihood estimation for problems in which missingness may be response‐related. These are typically simpler to implement than ordinary maximum likelihood, which in this context is semiparametric. Asymptotics for the pseudolikelihood methods are presented, and simulations conducted to investigate the methods for an important class of problems involving lifetime data. Our results indicate that for these problems the two methods are effective and comparable with respect to efficiency.
Fitting generalized linear models to retrospectively sampled clusters with categorical responses
Authors: Hines R.J. O'Hara
Published: June 2006

We use simulations based on data on injury severity in car accidents to compare methods for the analysis of very large data sets containing clusters of individuals for which the measured response is polytomous. Retrospective sampling of clusters is used to expedite the analysis of the large data set while at the same time obtaining information about rare, but important, outcomes. An additional complication in the analysis of such data sets is that there can be two types of covariates: those which vary within a cluster and those which vary only among clusters. Weighted generalized estimating equations are developed to obtain consistent estimates of the regression coefficients in a proportional‐odds model, along with a weighted robust covariance matrix to estimate the variabilities of these estimated coefficients.
Optimal designs for the logit and probit models for binary data
Authors: Sitter R. R. , Fainaru I.
Published: June 2006

We consider optimal designs for a class of symmetric models for binary data which includes the common probit and logit models. We show that for a large group of optimality criteria which includes the main ones in the literature (e.g.A‐, D‐, E‐, F‐andG‐optimality) the optimal design for our class of models is a two‐point design with support points symmetrically placed about the ED50 but with possibly unequal weighting. We demonstrate how one can further reduce the problem to a one‐variable optimization by characterizing various of the common criteria. We also use the results to demonstrate major qualitative differences between theF‐ andc‐optimal designs, two design criteria which have similar motivation.
Tests for noncorrelation of two multivariate ARMA time series
Authors: Himdi Khalid El , Roy Roch
Published: June 2006

In many situations, we want to verify the existence of a relationship between multivariate time series. In this paper, we generalize the procedure developed by Haugh (1976) for univariate time series in order to test the hypothesis of noncorrelation between two multivariate stationary ARMA series. The test statistics are based on residual cross‐correlation matrices. Under the null hypothesis of noncorrelation, we show that an arbitrary vector of residual cross‐correlations asymptotically follows the same distribution as the corresponding vector of cross‐correlations between the two innovation series. From this result, it follows that the test statistics considered are asymptotically distributed as chi‐square random variables. Two test procedures are described. The first one is based on the residual cross‐correlation matrix at a particular lag, whilst the second one is based on a portmanteau type statistic that generalizes Haugh's statistic. We also discuss how the procedures for testing noncorrelation can be adapted to determine the directions of causality in the sense of Granger (1969) between the two series. An advantage of the proposed procedures is that their application does not require the estimation of a global model for the two series. The finite‐sample properties of the statistics introduced were studied by simulation under the null hypothesis. It led to modified statistics whose upper quantiles are much better approximated by those of the corresponding chi‐square distribution. Finally, the procedures developed are applied to two different sets of economic data.
Cramér‐von Mises tests of fit for the Poisson distribution
Authors: Spinelli John J. , Stephens Michael A.
Published: June 2006

Goodness‐of‐fit tests based on the Cramér‐von Mises statistics are given for the Poisson distribution. Power comparisons show that these statistics, particularlyA2, give good overall tests of fit. The statisticA2will be particularly useful for detecting distributions where the variance is close to the mean, but which are not Poisson.
An adaptive test for the one‐way layout
Authors: O'GORMAN Thomas W.
Published: June 2006

An adaptive test is proposed for the one‐way layout. This test procedure uses the order statistics of the combined data to obtain estimates of percentiles, which are used to select an appropriate set of rank scores for the one‐way test statistic. This test is designed to have reasonably high power over a range of distributions. The adaptive procedure proposed for a one‐way layout is a generalization of an existing two‐sample adaptive test procedure. In this Monte Carlo study, the power and significance level of the F‐test, the Kruskal‐Wallis test, the normal scores test, and the adaptive test were evaluated for the one‐way layout. All tests maintained their significance level for data sets having at least 24 observations. The simulation results show that the adaptive test is more powerful than the other tests for skewed distributions if the total number of observations equals or exceeds 24. For data sets having at least 60 observations the adaptive test is also more powerful than the F‐test for some symmetric distributions.
The effect of mixing‐distribution misspecification in conjugate mixture models
Authors: Gustafson Paul
Published: June 2006

Parametric mixture models are commonly used in the analysis of clustered data. Parametric families are specified for the conditional distribution of the response variable given a cluster‐specific effect, and for the marginal distribution of the cluster‐specific effects. This latter distribution is referred to as the mixing distribution. If the form of the mixing distribution is misspecified, then Bayesian and maximum‐likelihood estimators of parameters associated with either distribution may be inconsistent. The magnitude of the asymptotic bias is investigated, using an approximation based on infinitesimal contamination of the mixing distribution. The approximation is useful when there is a closed‐form expression for the marginal distribution of the response under the assumed mixing distribution, but not under the true mixing distribution. Typically this occurs when the assumed mixing distribution is conjugate, meaning that the conditional distribution of the cluster‐specific parameter given the response variable belongs to the same parametric family as the mixing distribution.
Bayesian selection of log‐linear models
Authors: Albert James H.
Published: June 2006

A general methodology is presented for finding suitable Poisson log‐linear models with applications to multiway contingency tables. Mixtures of multivariate normal distributions are used to model prior opinion when a subset of the regression vector is believed to be nonzero. This prior distribution is studied for two‐ and three‐way contingency tables, in which the regression coefficients are interpretable in terms of odds ratios in the table. Efficient and accurate schemes are proposed for calculating the posterior model probabilities. The methods are illustrated for a large number of two‐way simulated tables and for two three‐way tables. These methods appear to be useful in selecting the best log‐linear model and in estimating parameters of interest that reflect uncertainty in the true model.
The residual effect of a growth‐decay mechanism and the distributions of covariance structures
Authors: Mathai A.M.
Published: June 2006

The product of two independent or dependent scalar normal variables, sums of products, sample covariances, and general bilinear forms are considered. Their distributions are shown to belong to a class called generalized Laplacian. A growth‐decay mechanism is also shown to produce such a generalized Laplacian. Sets of necessary and sufficient conditions are derived for bilinear forms to belong to this class. As a generalization, the distributions of rectangular matrices associated with multivariate normal random vectors are also discussed.
Interblock information in multidimensional block designs
Authors: Stewart Frances P. , Bradley Ralph A.
Published: June 2006

In many experimental situations, d‐way heterogeneity among experimental units may be controlled through use of multiple blocking criteria. In some cases it is reasonable to regard some or all of the block effects as random. Then the model is mixed and observations within blocks are correlated. Very general estimators of treatment effects and their dispersion matrix with recovery of interblock information are provided. They apply to designs with d > 1 blocking criteria that may be crossed, nested, or a combination thereof. These general results may be specialized to provide analyses of new classes of MBD's or used directly for numerical analyses of designs in the general class, perhaps through use as the basis for very general computer programs. Estimation of variance components is discussed, and an example is provided to illustrate adaptation of the general results.
Maximum‐likelihood estimation for constrained‐ or missing‐data models
Authors: Gelfand Alan E. , Carlin Bradley P.
Published: June 2006

In statistical models involving constrained or missing data, likelihoods containing integrals emerge. In the case of both constrained and missing data, the result is a ratio of integrals, which for multivariate data may defy exact or approximate analytic expression. Seeking maximum‐likelihood estimates in such settings, we propose Monte Carlo approximants for these integrals, and subsequently maximize the resulting approximate likelihood. Iteration of this strategy expedites the maximization, while the Gibbs sampler is useful for the required Monte Carlo generation. As a result, we handle a class of models broader than the customary EM setting without using an EM‐type algorithm. Implementation of the methodology is illustrated in two numerical examples.
Approximate Studentization with marginal and conditional inference
Authors: Fraser D.A.S. , Wong A.C.M.
Published: June 2006

Many inference problems lead naturally to a marginal or conditional measure of departure that depends on a nuisance parameter. As a device for first‐order elimination of the nuisance parameter, we suggest averaging with respect to an exact or approximate confidence distribution function. It is shown that for many standard problems where an exact answer is available by other methods, the averaging method reproduces the exact answer. Moreover, for the gamma‐mean problem, where the exact answer is not explicitly available, the averaging method gives results that agree closely with those obtained from higher‐order asymptotic methods. Examples are discussed; detailed asymptotic calculations will be examined elsewhere.
The reflected normal loss function
Authors: Spiring Fred A.
Published: June 2006

The use of loss functions in quality assurance has grown steadily with the introduction of Taguchi's philosophy. The quadratic loss function has been used by decision‐theoretic statisticians and economists for many years. Taguchi uses a modified form of the quadratic loss function to demonstrate the need to consider proximity to the target while assessing quality. Several authors have suggested that the traditional quadratic loss function is inadequate for assessing quality and quality improvement. A new, easily understood loss function, based on a reflection of the normal density function, is presented, and some associated statistical properties discussed.
A new class of measurement‐error models, with applications to dietary data
Authors: Carroll Raymond J. , Freedman Laurence S. , Kipnis Victor , Li Li
Published: June 2006

Measurement‐error modelling occurs when one cannot observe a covariate, but instead has possibly replicated surrogate versions of this covariate measured with error. The vast majority of the literature in measurement‐error modelling assumes (typically with good reason) that given the value of the true but unobserved (latent) covariate, the replicated surrogates are unbiased for latent covariate and conditionally independent. In the area of nutritional epidemiology, there is some evidence from biomarker studies that this simple conditional independence model may break down due to two causes: (a) systematic biases depending on a person's body mass index, and (b) an additional random component of bias, so that the error structure is the same as a one‐way random‐effects model. We investigate this problem in the context of (1) estimating distribution of usual nutrient intake, (2) estimating the correlation between a nutrient instrument and usual nutrient intake, and (3) estimating the true relative risk from an estimated relative risk using the error‐prone covariate. While systematic bias due to body mass index appears to have little effect, the additional random effect in the variance structure is shown to have a potentially important effect on overall results, both on corrections for relative risk estimates and in estimating the distribution of usual nutrient intake. However, the effect of dietary measurement error on both factors is shown via examples to depend strongly on the data set being used. Indeed, one of our data sets suggests that dietary measurement error may be masking a strong risk of fat on breast cancer, while for a second data set this masking is not so clear. Until further understanding of dietary measurement is available, measurement‐error corrections must be done on a study‐specific basis, sensitivity analyses should be conducted, and even then results of nutritional epidemiology studies relating diet to disease risk should be interpreted cautiously.
A sequential design for maximizing the probability of a favourable response
Authors: Durham S.D. , Flournoy N. , Li W.
Published: June 2006

Consider the situation in which subjects arrive sequentially for a treatment and in which there are two distinct ways in which the treatment may fail. Treatments are given at different dosages, and the probabilities of the two failure types vary with dose. Assuming that decreasing the chances of one failure type increases the chances of the other, we say the failures oppose each other. Also assume that one failure type is primary in that, if it occurs, it censors the trial, so that observation of the secondary failure type is contingent on no failure of the primary type. We are interested in designs that provide information about the dose that maximizes the probability of success, i.e., the optimal dose, while treating very few subjects at dosages that have high risks of failure. Assuming that dosages belong to a discrete set, we show that a randomized version of the Pólya urn scheme causes dose selection to be progressively biased so as to favour those doses that produce success with higher probability.
LTD and RTI dependence orderings
Authors: Averous Jean , Dortet‐Bernadet Jean‐Luc
Published: June 2006

The authors show how the approach of Capéra à & Genest (The Canadian Journal of Statistics, 1990) can be used to order bivariate distributions with arbitrary marginals by their degree of dependence in the LTD (left‐tail decreasing) or RTI (right‐tail increasing) sense. Some properties of these new orderings are given, along with applications to Archimedean copulas, order statistics and compound random variables.
On the asymptotics of randomness statistics
Authors: Mcdonald D.
Published: June 2006

Kiefer (1959) studied the asymptotics of q‐sample Cramér‐von Mises nonparametric statistics when q is fixed and the sample sizes tend to infinity. Here we prove the asymptotic normality of such statistics when the sample sizes stay fixed or small while the number of samples, q, becomes large.
An inclusion‐consistent solution to the problem of absurd confidence statements: 2. Consistent nonexact‐confidence‐interval estimation
Authors: Plante André
Published: June 2006

Two consistent nonexact‐confidence‐interval estimation methods, both derived from the consistency‐equivalence theorem in Plante (1991), are suggested for estimation of problematic parametric functions with no consistent exact solution and for which standard optimal confidence procedures are inadequate or even absurd, i.e., can provide confidence statements with a 95% empty or all‐inclusive confidence set. A belt C(·) from a consistent nonexact‐belt family, used with two confidence coefficients (γ = infθ Pθ [ θ ϵ C(X)] and γ+ = supθ Pθ[θ ϵ C(X)], is shown to provide a consistent nonexact‐belt solution for estimating μ2 ‐μ1 in the Behrens‐Fisher problem. A rule for consistent behaviour enables any confidence belt to be used consistently by providing each sample point with best upper and lower confidence levels [δ+(x) ≥ γ+, δ(x) ≤ γ], which give least‐conservative consistent confidence statements ranging from practically exact through informative to noninformative. The rule also provides a consistency correction L(x) = δ+(x)‐δ(X) enabling alternative confidence solutions to be compared on grounds of adequacy; this is demonstrated by comparing consistent conservative sample‐point‐wise solutions with inconsistent standard solutions for estimating μ2/μ1 (Creasy‐Fieller‐Neyman problem) and \documentclass{article}\pagestyle{empty}\begin{document}$\sqrt {\mu _1^2 + \mu _2^2 }$\end{document}, a distance‐estimation problem closely related to Stein's 1959 example
Information, ancillarity, and sufficiency in the presence of nuisance parameters
Authors: Zhu Yiliang , Reid Nancy
Published: June 2006

The Fisher information about parameters of interest (P‐information) is invariant with respect to nuisance parameters, and induces an information inequality associated with likelihood factorization. This information inequality provides a natural basis for measuring information loss due to using only a sublikelihood function for inference. In contrast with the global reparametrization of some previous concepts in the literature, the concepts of P‐ancillarity and P‐sufficiency proposed in this article are characterized by the notion of no pointwise information loss with respect to the parameters of interest. A conditional version of P‐sufficiency is also proposed. The asymptotic efficiency of likelihood inference under P‐ancillarity or P‐sufficiency is outlined.
Design and analysis of computer experiments when the output is highly correlated over the input space
Authors: Lim Yong B. , Sacks Jerome , Studden W. J. , Welch William J.
Published: June 2006

To build a predictor, the output of a deterministic computer model or “code” is often treated as a realization of a stochastic process indexed by the code's input variables. The authors consider an asymptotic form of the Gaussian correlation function for the stochastic process where the correlation tends to unity. They show that the limiting best linear unbiased predictor involves Lagrange interpolating polynomials; linear model terms are implicitly included. The authors then develop optimal designs based on minimizing the limiting integrated mean squared error of prediction. They show through several examples that these designs lead to good prediction accuracy.
Bounds on the maximum number of clear two‐factor interactions for 2m‐p designs of resolution III and IV
Authors: Tang Boxin , Ma Fengshi , Ingram Debra , Wang Hong
Published: June 2006

The authors derive upper and lower bounds on the maximum number of clear two‐factor interactions in 2m−p fractional factorial designs of resolution III and IV. A two‐factor interaction is said to be clear if it is not aliased with any main effect or with any other two‐factor interaction. The lower bounds are obtained by exhibiting specific designs. By comparing the bounds with the values of the maximum number of clear two‐factor interactions in cases where it is known, one concludes that the construction methods perform quite well.
Median estimation through a regression transformation
Authors: Yang Zhenlin
Published: June 2006

The author considers the problem of constructing confidence intervals for the median of a future observation at certain values of exogenous variables, following a normalizing transformation. He shows that when this transformation is estimated, the usual interval obtained through an inverse transformation needs to be corrected, even when the sample size is large. He then gives a simple analytical solution to this problem and provides simulation results confirming the good small‐sample properties of the corrected interval. He also presents two concrete illustrations.
Minimax A‐ and D‐optimal integer‐valued wavelet designs for estimation
Authors: Oyet Alwell J.
Published: June 2006

The author discusses integer‐valued designs for wavelet estimation of nonparametric response curves in the possible presence of heteroscedastic noise using a modified wavelet version of the Gasser‐Müller kernel estimator or weighted least squares estimation. The designs are constructed using a minimax treatment and the simulated annealing algorithm. The author presents designs for three case studies in experiments for investigating Gompertz's theory on mortality rates, nitrite utilization in bush beans and the impact of crash helmets in motorcycle accidents.
Stabilizing bootstrap‐tconfidence intervals for small samples
Authors: Polansky Alan M.
Published: June 2006

A major use of the bootstrap methodology is in the construction of nonparametric confidence intervals. Although no consensus has yet been reached on the best way to proceed, theoretical and empirical evidence indicate that bootstra.‐tintervals provide a reasonable solution to this problem. However, when applied to small data sets, these intervals can be unusually wide and unstable. The author presents techniques for stabilizing bootstra.‐tintervals for small samples. His methods are motivated theoretically and investigated though simulations.
Score tests for zero inflation in generalized linear models
Authors: Deng Dianliang , Paul Sudhir R.
Published: June 2006

The authors develop score tests of goodness of fit for discrete generalized linear models against zero inflation. The binomial and Poisson models are treated as examples, and in the latter case the proposed test reduces to that of Broek (1995). Some simulation results and an illustrative example are presented.
Inférence par les martingales pour des processus ponctuels à compensateur discontinu
Authors: Dauxois Jean‐Yves
Published: June 2006

L'auteur introduit un modèle d'intensité mutltiplicative généralisé pour les processus ponctuels à compensateur discontinu. Il en étudie l'inférence par les martingales et obtient un résultat de normalité asymptotique. Il applique ces résultats à l'estimateur de Nelson‐Aalen du taux de panne cumulé dans le cas de données de durée de vie censuées et de loi non nécessairement continues.
Monte Carlo Kalman filter and smoothing for multivariate discrete state space models
Authors: Song Peter Xue‐Kun
Published: June 2006

The author studies state space models for multivariate binomial time series, focussing on the development of the Kalman filter and smoothing for state variables. He proposes a Monte Carlo approach employing the latent variable representation which transplants the classical Kalman filter and smoothing developed for Gaussian state space models to discrete models and leads to a conceptually simple and computationally convenient approach. The method is illustrated through simulations and concrete examples.
Nonparametric two‐step regression estimation when regressors and error are dependent
Authors: Pinkse Jons
Published: June 2006

This paper considers estimation of the functiongin the modelYt=g(Xt) + ϵtwhen E(ϵt|Xt) ≠ 0 with nonzero probability. We assume the existence of aninstrumental variable Ztthat is independent of ϵt, and of aninnovationηt=Xt—E(Xt|Zt). We use a nonparametric regression ofXtonZtto obtain residuals ηt, which in turn are used to obtain a consistent estimator ofg. The estimator was first analyzed by Newey, Powell & Vella (1999) under the assumption that the observations are independent and identically distributed. Here we derive a sample mean‐squared‐error convergence result for independent identically distributed observations as well as a uniform‐convergence result under time‐series dependence.
Nonparametric regression for threshold data
Authors: Müller Ursula U.
Published: June 2006

Consider a detector which records the times at which the endogenous variable of a nonparametric regression model exceeds a certain threshold. If the error distribution is known, the regression function can still be identified from these threshold data. The author constructs estimators for the regression function that are transformations of kernel estimators. She determines the bandwidth that minimizes the asymptotic mean average squared error. Her investigation was motivated by recent work on stochastic resonance in neuroscience and signal detection theory, where it was observed that detection of a subthreshold signal is enhanced by the addition of noise. The author compares her model with several others that have been proposed in the recent past.
Bayesian assessment of goodness of fit against nonparametric alternatives
Authors: Conigliani Caterina , Castro J. Iván , O'HAGAN Anthony
Published: June 2006

The classical chi‐square test of goodness of fit compares the hypothesis that data arise from some parametric family of distributions, against the nonparametric alternative that they arise from some other distribution. However, the chi‐square test requires continuous data to be grouped into arbitrary categories. Furthermore, as the test is based upon an approximation, it can only be used if there are sufficient data. In practice, these requirements are often wasteful of information and overly restrictive. The authors explore the use of the fractional Bayes factor to obtain a Bayesian alternative to the chi‐square test when no specific prior information is available. They consider the extent to which their methodology can handle small data sets and continuous data without arbitrary grouping.
Estimating the number of clusters
Authors: Cuevas Antonio , Febrero Manuel , Fraiman Ricardo
Published: June 2006

Hartigan (1975) defines the numberqof clusters in ad‐variate statistical population as the number of connected components of the set {f> c}, wherefdenotes the underlying density function on Rdandcis a given constant. Some usual cluster algorithms treatqas an input which must be given in advance. The authors propose a method for estimating this parameter which is based on the computation of the number of connected components of an estimate of {f> c}. This set estimator is constructed as a union of balls with centres at an appropriate subsample which is selected via a nonparametric density estimator off. The asymptotic behaviour of the proposed method is analyzed. A simulation study and an example with real data are also included.
On the distribution of linear combinations of the components of a Dirichlet random vector
Authors: Provost Serge B. , Cheong Young‐Ho
Published: June 2006

On making use of a result of Imhof, an integral representation of the distribution function of linear combinations of the components of a Dirichlet random vector is obtained. In fact, the distributions of several statistics such as Moran and Geary's indices, the Cliff‐Ord statistic for spatial correlation, the sample coefficient of determination, F‐ratios and the sample autocorrelation coefficient can be similarly determined. Linear combinations of the components of Dirichlet random vectors also turn out to be a key component in a decomposition of quadratic forms in spherically symmetric random vectors. An application involving the sample spectrum associated with series generated by ARMA processes is discussed.
Implications of random cut‐points theory for the Mann‐Whitney and binomial tests
Authors: Edwardes Michael D.Deb.
Published: June 2006

Through random cut‐points theory, the author extends inference for ordered categorical data to the unspecified continuum underlying the ordered categories. He shows that a random cut‐point Mann‐Whitney test yields slightly smaller p‐values than the conventional test for most data. However, when at least P% of the data lie in one of the k categories (with P = 80 for k = 2, P = 67 for k = 3,…, P = 18 for k = 30), he also shows that the conventional test can yield much smaller p‐values, and hence misleadingly liberal inference for the underlying continuum. The author derives formulas for exact tests; for k = 2, the Mann‐Whitney test is but a binomial test.
Authors' addendum to: “A generalized‐moments specification test for the logistic link”
Authors: Fokianos Konstantinos , Peng Amy , Qin Jing
Published: June 2006

The Candian Journal of Statistics, Vol. 27, No. 4, 1999, pp. 735‐750.
A nonparametric test of conditional autoregressive heteroscedasticity for threshold autoregressive models
Authors: Chen Min , Chen Gemai
Published: June 2006

Threshold autoregressive models are widely used in time‐series applications. When building or using such a model, it is important to know whether conditional heteroscedasticity exists. The authors propose a nonparametric test of this hypothesis. They develop the large‐sample theory of a test of nonlinear conditional heteroscedasticity adapted to nonlinear autoregressive models and study its finite‐sample properties through simulations. They also provide percentage points for carrying out this test, which is found to have very good power overall.
Extrapolation of subsampling distribution estimators: The i.i.d. and strong mixing cases
Authors: Bertail Patrice , Politis Dimitris N.
Published: June 2006

Politis & Romano (1994) proposed a general subsampling methodology for the construction of large‐sample confidence regions for an arbitrary parameter under minimal conditions. Nevertheless, the subsampling distribution estimators may sometimes be inefficient (in the case of the sample mean of i.i.d. data, for instance) as compared to alternative estimators such as the bootstrap and/or the asymptotic normal distribution (with estimated variance). The authors investigate here the extent to which the performance of subsampling distribution estimators can be improved by interpolation and extrapolation techniques, while at the same time retaining the robustness property of consistent distribution estimation even in nonregular cases; both i.i.d. and weakly dependent (mixing) observations are considered.
Flexible regression modeling
Authors: Hooper Peter M.
Published: June 2006

The author proposes a new method for flexible regression modeling of multi‐dimensional data, where the regression function is approximated by a linear combination of logistic basis functions. The method is adaptive, selecting simple or more complex models as appropriate. The number, location, and (to some extent) shape of the basis functions are automatically determined from the data. The method is also affine invariant, so accuracy of the fit is not affected by rotation or scaling of the covariates. Squared error and absolute error criteria are both available for estimation. The latter provides a robust estimator of the conditional median function. Computation is relatively fast, particularly for large data sets, so the method is well suited for data mining applications.
Estimation of relaxation time distributions in magnetic resonance imaging
Authors: Susko Edward , Bronskill Michael J. , Graham Simon J. , Tibshirani Robert J.
Published: June 2006

Magnetic resonance imaging techniques can be used to measure some biophysical properties of tissue. In this context, the T2 relaxation time is an important parameter for soft‐tissue contrast. The authors develop a new technique to estimate the integral of the distribution of T2 relaxation time without imposing any constraint other than the monotonicity of the underlying cumulative relaxation time distribution. They explore the properties of the estimation and its applications for the analysis of breast tissue data. As they show, an extension of linear discriminant analysis is found to distinguish well between two classes of breast tissue.
On the polynomial structural relationship
Authors: Huang Y. H. Steve , Huwang Longcheen
Published: June 2006

In estimating a linear measurement error model, extra information is generally needed to identify the model. Here the authors show that the polynomial structural model with errors in the endogenous and exogenous variables can be identified without any extra information if the degree is greater than one. They also show that a weighted least squares approach for the estimation of the parameters in the model leads to the same estimates as the solutions of a system of estimating equations.
An adaptive randomized design with application to estimation
Authors: Melfi Vincent F. , Page Connie , Geraldes Margarida
Published: June 2006

When allocating observations to two populations for estimation or testing, the optimal proportion of the data that should be allocated to the first population, if it exists, often depends on unknown parameters. Adaptive designs have thus been proposed, in which allocation of the next observation is based on an estimate of the optimal proportion computed from the data already gathered. The authors introduce a simple randomized adaptive design and give some of its properties. Applications are given to estimating the difference of two success probabilities, and the difference of two normal means.
Variance estimation for the finite population distribution function with complete auxiliary information
Authors: Wu Changbao , Sitter Randy R.
Published: June 2006

The authors develop jackknife and analytical variance estimators for the estimator of Chambers & Dunstan (1986) and Rao, Kovar & Mantel (1990) of the finite population distribution function, using complete auxiliary information. They also describe the associated model and show the design consistency of the variance estimators, whose small‐sample performance is examined through a limited simulation study. They highlight the operational advantages of the jackknife in the model‐based setting of Chambers & Dunstan (1986) and its better conditional performance in the design‐based setting of Rao, Kovar & Mantel (1990).
Statistical analyses for round robin interaction data
Authors: Gill Paramjit S. , Swartz Tim B.
Published: June 2006

This paper considers the analysis of round robin interaction data whereby individuals from a group of subjects interact with one another, producing a pair of outcomes, one for each individual. The authors provide an overview of the various analyses applied to these types of data and extend the work in several directions. In particular, they provide a fully Bayesian analysis for such data and use a real data example for illustration purposes.
On cross‐validation of Bayesian models
Authors: Alqallaf Fatemah , Gustafson Paul
Published: June 2006

The authors examine several aspects of cross‐validation for Bayesian models. In particular, they propose a computational scheme which does not require a separate posterior sample for each training sample.
A glimpse of the impact of pál erd#ous on probability and statistics
Authors: CsõRGõ MiklÓS
Published: June 2006

The title of this article notwithstanding, it is the author's aspiration here to provide a bit more than merely a glimpse of some of Erdõs's contributions per se to probability‐statistics. He hopes to have succeeded in providing a guided tour of, and whenever it has appeared feasible, an introduction to, a few selected areas that have been strongly influenced by the work of Erdõs. The author also hopes to have succeeded in facilitating a glimpse of the impact of these contributions by presenting them in their historical context.
Quotient spaces and statistical models
Authors: Mccullagh Peter
Published: June 2006

The purpose of this paper is to draw attention to the widespread occurrence of quotient spaces in statistical work. Quotient spaces are intrinsic to probability distributions, residuals and interaction in linear models, covariance functions and variograms of stochastic processes, etc. The theme is that explicit recognition of the quotient space can offer surprising conceptual simplification. The advantages of working directly with the quotient space are hard to describe in general. As the examples demonstrate, the answer lies partly in directness of approach.
Asymptotic behavior of the grenander estimator at density flat regions
Authors: Carolan Chris , Dykstra Richard
Published: June 2006

Over forty years ago, Grenander derived the MLE of a monotone decreasing density f with known mode. Prakasa Rao obtained the asymptotic distribution of this estimator at a fixed point x where f' (x) < 0. Here, we obtain the asymptotic distribution of this estimator at a fixed point x when f is constant and nonzero in some open neighborhood of x. This limiting distribution is expressible as the convolution of a closed‐form density and a rescaled standard normal density. Groeneboom (1983) derived the aforementioned closed‐form density and we provide an alternative, more direct derivation.
Dirichlet forms: Some infinite‐dimensional examples
Authors: Schmuland Byron
Published: June 2006

The author presents three examples of a Markov process taking values in an infinite‐dimensional state space and analyzes the sample path behaviour using the theory of Dirichlet forms.
Semiparametric Bayesian inference for regression models
Authors: Seifu Yodit , Severini Thomas A. , Tanner Martin A.
Published: June 2006

This paper presents a method for Bayesian inference for the regression parameters in a linear model with independent and identically distributed errors that does not require the specification of a parametric family of densities for the error distribution. This method first selects a nonparametric kernel density estimate of the error distribution which is unimodal and based on the least‐squares residuals. Once the error distribution is selected, the Metropolis algorithm is used to obtain the marginal posterior distribution of the regression parameters. The methodology is illustrated with data sets, and its performance relative to standard Bayesian techniques is evaluated using simulation results.
Conditional logspline density estimation
Authors: Mâacsse Benoît R. , Truong Young K.
Published: June 2006

Inconditional logspline modelling, the logarithm of the conditional density function, logf(y|x), is modelled by using polynomial splines and their tensor products. The parameters of the model (coefficients of the spline functions) are estimated by maximizing the conditional log‐likelihood function. The resulting estimate is a density function (positive and integrating to one) and is twice continuously differentiable. The estimate is used further to obtain estimates of regression and quantile functions in a natural way. An automatic procedure for selecting the number of knots and knot locations based on minimizing a variant of the AIC is developed. An example with real data is given. Finally, extensions and further applications of conditional logspline models are discussed.
Fisher information in weighted distributions
Authors: Iyengar Satish , Kvam Paul , Singh Harshinder
Published: June 2006

Suppose that a density fθ (x) belongs to an exponential family, but that inference about θ must be based on data that are obtained from a density that is proportional to W(x)fθ(x). The authors study the Fisher information about θ in observations obtained from such weighted distributions and give conditions under which this information is greater than under the original density. These conditions involve the hazard‐ and reversed‐hazard‐rate functions.
A similarity analysis of curves
Authors: Maldonado Yolanda MuÑoz , Staniswalis Joan G. , Irwin Louis N. , Byers Donna
Published: June 2006

The authors propose a method for comparing two samples of curves. The notion of similarity between two curves is the basis of three statistics they suggest for testing the null hypothesis of no difference between the two groups. They exploit standard tools from functional data analysis to preprocess the observed curves and use the permutation distribution under the null hypothesis to obtain p‐values for their tests. They explore the operating characteristics of these tests through simulations and as an application, compare the ganglioside distribution in brain tissue between old and young rats.
Estimation of a residual distribution with small numbers of repeated measurements
Authors: Susko Edward , Nadon Robert
Published: June 2006

The authors consider the estimation of a residual distribution for different measurement problems with a common measurement error process. The problem is motivated by issues arising in the analysis of gene expression data but should have application in other similar settings. It is implicitly assumed throughout that there are large numbers of measurements but small numbers of repeated measurements. As a consequence, the distribution of the estimated residuals is a biased estimate of the residual distribution. The authors present two methods for the estimation of the residual distribution with some restriction on the form of the distribution. They give an upper bound for the rate of convergence for an estimator based on the characteristic function and compare its performance with that of another estimator with simulations.