bluuebunny/crossref_metadata_2025_split huggingface dataset:
Concepts and measures for skewness with data‐analytic implications
Authors: Benjamini Yoav , Krieger Abba M. 
Published: June 2006

AbstractThe 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

AbstractOja (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

AbstractWe 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

AbstractWe 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

AbstractWe 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

AbstractMany 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

AbstractWe 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

AbstractWe 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

AbstractIn 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

AbstractGoodness‐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

AbstractAn 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

AbstractParametric 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

AbstractA 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

AbstractThe 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

AbstractIn 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

AbstractIn 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

AbstractMany 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

AbstractThe 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

AbstractMeasurement‐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

AbstractConsider 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

AbstractThe 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

AbstractKiefer (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

AbstractTwo 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

AbstractThe 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.