bluuebunny/crossref_metadata_2025_split huggingface dataset:
On approximate likelihood inference in a poisson mixed model
Authors: Sutradhar Brajendra C. , Qu Zhende 
Published: June 2006

AbstractA two‐step estimation approach is proposed for the fixed‐effect parameters, random effects and their variance σ2of a Poisson mixed model. In the first step, it is proposed to construct a small σ2‐based approximate likelihood function of the data and utilize this function to estimate the fixed‐effect parameters and σ2. In the second step, the random effects are estimated by minimizing their posterior mean squared error. Methods of Waclawiw and Liang (1993) based on so‐called Stein‐type estimating functions and of Breslow and Clayton (1993) based on penalized quasilikelihood are compared with the proposed likelihood method. The results of a simulation study on the performance of all three approaches are reported.
Estimating conditional occupation‐time distributions for dependent sequences
Authors: Dabrowski André Robert , Dehling Herold 
Published: June 2006

AbstractConsider a random integer‐valued processX(t) onZ+that satisfies some weak dependence condition. We study the empirical distribution function of the occupation times of such a process and prove convergence to a suitable Gaussian process. An application to the statistical analysis of open and closed sojourn‐time distributions for ion channels is provided.
Analysis of interval‐grouped recurrent‐event data using piecewise constant rate functions
Authors: Lawless J. F. , Zhan M. 
Published: June 2006

AbstractWe consider situations where subjects in a longitudinal study experience recurrent events. However, the events are observed only in the form of counts for intervals which can vary across subjects. Methods for estimating the mean and rate functions of the recurrent‐event processes are presented, based on loglinear regression models which incorporate piecewise‐constant baseline rate functions. Robust methods and methods based on mixed Poisson processes are compared in a simulation study and in an example involving superficial bladder tumours in humans. Both approaches provide a simple and effective way to deal with interval‐grouped data.
Penalized likelihood‐ratio test for finite mixture models with multinomial observations
Authors: Chen Jiahua 
Published: June 2006

AbstractDue to the irregularity of finite mixture models, the commonly used likelihood‐ratio statistics often have complicated limiting distributions. We propose to add a particular type of penalty function to the log‐likelihood function. The resulting penalized likelihood‐ratio statistics have simple limiting distributions when applied to finite mixture models with multinomial observations. The method is especially effective in addressing the problems discussed by Chernoff and Lander (1995). The theory developed and simulations conducted show that the penalized likelihood method can give very good results, better than the well‐known C(α) procedure, for example. The paper does not, however, fully explore the choice of penalty function and weight. The full potential of the new procedure is to be explored in the future.
Slow convergence of the Gibbs sampler
Authors: Bélisle Claude 
Published: June 2006

AbstractWe consider the Gibbs sampler as a tool for generating an absolutely continuous probability measure ≥ onRd. When an appropriate irreducibility condition is satisfied, the Gibbs Markov chain (Xn;n ≥ 0) converges in total variation to its target distribution ≥. Sufficient conditions for geometric convergence have been given by various authors. Here we illustrate, by means of simple examples, how slow the convergence can be. In particular, we show that given a sequence of positive numbers decreasing to zero, say (bn;n≥ 1), one can construct an absolutely continuous probability measure ≥ on Rdwhich is such that the total variation distance between ≥ and the distribution ofXn, converges to 0 at a rate slower than that of the sequence (bn;n≥ 1). This can even be done in such a way that ≥ is the uniform distribution over a bounded connected open subset ofRd. Our results extend to hit‐and‐run samplers with direction distributions having supports with symmetric gaps.
A bayesian approach to a reliability problem: Theory, analysis and interesting numerics
Authors: Guttman Irwin , Papandonatos George D. 
Published: June 2006

AbstractWe consider approximate Bayesian inference about the quantityR=P[Y2>Y1] when both the random variablesY1,Y2have expectations that depend on certain explanatory variables. Our interest centers on certain characteristics of the posterior ofRunder Jeffreys's prior, such as its mean, variance and percentiles. Since the posterior ofRis not available in closed form, several approximation procedures are introduced, and their relative performance is assessed using two real datasets.
Supersaturated design including an orthogonal base
Authors: Yamada Shu , Un Dennis K. J. 
Published: June 2006

AbstractRecently, many supersaturated designs have been proposed. A supersaturated design is a fractional factorial design in which the number of factors is greater than the number of experimental runs. The main thrust of the previous studies has been to generate more columns while avoiding large values of squared inner products among all design columns. These designs would be appropriate if the probability for each factor being active is uniformly distributed. When factors can be partitioned into two groups, namely, with high and low probabilities of each factor being active, it is desirable to maintain orthogonality among columns to be assigned to the factors in the high‐probability group. We discuss a supersaturated design including an orthogonal base which is suitable for this common situation. Mathematical results on the existence of the supersaturated designs are shown, and the construction of supersaturated designs is presented. We next discuss some properties of the proposed supersaturated designs based on the squared inner products.
Analysis of overdispersed paired count data
Authors: Lee Hyun Suk 
Published: June 2006

AbstractThis article is about the statistical analysis of overdispersed paired count data for comparing two treatments. The data consist of the number of events obtained in a stratum during the fixed observation period. Three types of model are discussed: the Poisson, a mixed, and a semiparametric model. Overdispersion is represented in the last two models but not in the Poisson model. Of particular interests are to examine whether there is any loss of efficiency in using the estimate of the treatment effect obtained under other two models if the mixed model is true, and also whether overdispersion leads to a larger variance of the estimate than that expected from the Poisson model. It is shown that all three models provide the same estimate of the treatment effect (i.e., there is no loss of efficiency) and that the variance of the estimate of the treatment effect obtained under the Poisson model is the same as that based on the mixed model. However, the semiparametric model provides the variance of the estimate larger than those obtained under the other two models.
EDF tests of goodness of fit for transform‐both‐sides models
Authors: Chen Gemai 
Published: June 2006

AbstractVery often in regression analysis, a particular functional form connecting known covariates and unknown parameters is either suggested by previous work or demanded by theoretical considerations so that the deterministic part of the responses has a known form. However, the underlying error structure is often less well understood. In this case, the transform‐both‐sides (TBS) models are appropriate. In this paper we generalize the usual TBS models and develop tests to assess goodness of fit when fitting TBS or GTBS models. Parameter estimation is discussed, and tests based on the Cramér‐von Mises statistic and the Anderson‐Darling statistic are presented with a table suitable for finite‐sample applications.
State‐space models for multivariate longitudinal data of mixed types
Authors: Jørgensen Bent , Lundbye‐Christensen Søren , Song Peter Xue‐Kun , Sun Li 
Published: June 2006

AbstractWe propose a class of state‐space models for multivariate longitudinal data where the components of the response vector may have different distributions. The approach is based on the class of Tweedie exponential dispersion models, which accommodates a wide variety of discrete, continuous and mixed data. The latent process is assumed to be a Markov process, and the observations are conditionally independent given the latent process, over time as well as over the components of the response vector. This provides a fully parametric alternative to the quasilikelihood approach of Liang and Zeger. We estimate the regression parameters for time‐varying covariates entering either via the observation model or via the latent process, based on an estimating equation derived from the Kalman smoother. We also consider analysis of residuals from both the observation model and the latent process.
On the role of statistics in the palaeomagnetic proof of continental drift
Authors: Watson Geoffrey 
Published: June 2006

AbstractMagnetized rocks provide a “tape recording” of the more recent history of the earth. It was this evidence that broke the opposition to continental drift. The nature of the data ‐ samples of unit vectors in three dimensions ‐ demanded new forms of statistical treatment. I hope that my personal account will enable the general statistician to see a rare example of statistics being developed to be a modest help in a major scientific revolution.
Elephant‐seal movements: Modelling migration
Authors: Brillinger David R. , Stewart Brent S. 
Published: June 2006

AbstractElephant seals migrate over vast areas of the eastern North Pacific Ocean between rookeries in southern California and distant northern foraging areas. Several models of particle movement were evaluated and a model for great‐circle motion found to give reasonable results for the movement of an adult female. This model takes specific account of the fact that the movement is on the surface of a sphere and that the animal is apparently heading toward a particular destination. The parameters of the motion were estimated. Such a great‐circle path of migration may imply that these seals have the ability to assess their position with respect to some global or celestial cues, allowing them to continually adjust their course and achieve the most direct geodesic route between origin and destination of migration. But the navigational mechanism actually used by these seals to accomplish such feats is as yet unknown.
Statistical methodology for assessing homology of intronic regions of genes
Authors: Hall Deborah L. , Kafadar Karen , Malkinson Alvin M. 
Published: June 2006

AbstractWe consider the problem of statistically evaluating the similarity of DNA intronic regions of genes. Present algorithms are based on matching a sequence of interest with known DNA sequences in a gene bank and are designed primarily to assess homology among exonic regions of genes. Most research focuses on exonic regions because they have a clear biological significance, coding for proteins, and therefore tend to be more conserved in evolution than intronic regions. To investigate whether the intronic features of genes whose expression is highly sensitive to environmental perturbations differ from genes that have a more constant expression, a collection of oncogenes, tumor suppressor genes, and nonregulatory genes involved in energy metabolism are compared. An analysis of the features of these genes' intronic regions result in clustering by regulatory group. In addition, Billingsley's test for Markov structure (1961) suggests that 67% of the intronic regions in this collection of genes show evidence of nonrandom structure, indicating the possibility of a biological function for these regions. The result of Billingsley's test for homology is used as input to a clustering algorithm. The biological significance of this methodology lies in the identification of groups based on the intronic regions from genes of unknown function. With the advent of rapid sequencing techniques, there is a great need for statistical techniques to help identify the purpose of poorly understood portions of genes. These methods can be utilized to assess the functional group to which such a gene might possibly belong.
Is statistics too difficult?
Authors: Hampel Frank , Zurich Eth 
Published: June 2006

AbstractBy means of several historical examples, it is shown that it does not appear to be easy to build bridges between rigorous mathematics and reasonable data‐analytic procedures for scientific measurements. After mentioning both some positive and some negative aspects of statistics, a formal framework for statistics is presented which contains the concept formation, derivation of results and interpretation of mathematical statistics as three essential steps. The difficulties especially of interpretation are shown for examples in several areas of statistics, such as asymptotics and robustness. Some problems of statistics in two subject‐matter sciences are discussed, and a summary and outlook are given.
Estimation de densités unimodales
Authors: Fougères Anne‐Laure 
Published: June 2006

AbstractThis paper proposes a new nonparametric unimodal estimator of a unimodal probability density function, in the case where the mode is known. The classical solution to this problem is the maximum‐likelihood estimator under monotonicity constraint, considered by Grenander (1956). Our approach is based on a unimodal rearrangement of the kernel estimator of the density. Asymptotic properties of this estimator are studied, and its small‐sample behaviour is examined through simulations.
Confidence intervals following Box‐Cox transformation
Authors: Hooper Peter M. , Yang Zhenlin 
Published: June 2006

AbstractWhat is the interpretation of a confidence interval following estimation of a Box‐Cox transformation parameter λ? Several authors have argued that confidence intervals for linear model parameters ψ can be constructed as if λ. were known in advance, rather than estimated, provided the estimand is interpreted conditionally given\documentclass{article}\pagestyle{empty}\begin{document}$\hat \lambda$\end{document}. If the estimand is defined as\documentclass{article}\pagestyle{empty}\begin{document}$\psi \left( {\hat \lambda } \right)$\end{document}, a function of the estimated transformation, can the nominal confidence level be regarded as a conditional coverage probability given\documentclass{article}\pagestyle{empty}\begin{document}$\hat \lambda$\end{document}, where the interval is random and the estimand is fixed? Or should it be regarded as an unconditional probability, where both the interval and the estimand are random? This article investigates these questions via large‐napproximations, small‐ σ approximations, and simulations. It is shown that, when model assumptions are satisfied andnis large, the nominal confidence level closely approximates the conditional coverage probability. Whennis small, this conditional approximation is still good for regression models with small error variance. The conditional approximation can be poor for regression models with moderate error variance and single‐factor ANOVA models with small to moderate error variance. In these situations the nominal confidence level still provides a good approximation for the unconditional coverage probability. This suggests that, while the estimand may be interpreted conditionally, the confidence level should sometimes be interpreted unconditionally.
Finite‐population prediction under error‐in‐variables superpopulation models
Authors: Bolfarine Heleno 
Published: June 2006

AbstractThe prediction problem in finite populations is considered under error‐in‐variables super population models. The models considered are the usual regression models involving at most two variables,xandy, where both may be measured with error. Properties of some classical predictors are investigated. A Bayesian approach is proposed.
Contre‐exemple au théorème de P.C. Consul sur la factorisation des distributions de Poisson généralisées
Authors: Letac Gérard 
Published: June 2006

AbstractThis note exhibits two independent random variables on integers, X1 and X2, such that neither X1 nor X2 has a generalized Poisson distribution, but X1 + X2 has. This contradicts statements made by Professor Consul in his recent book.
Some aspects of the reparametrization of statistical models
Authors: Tibshirani Robert , Wasserman Larry 
Published: June 2006

AbstractDefinitions are given for orthogonal parameters in the context of Bayesian inference and likelihood inference. The exact orthogonalizing transformations are derived for both cases, and the connection between the two settings is made precise. These parametrizations simplify the interpretation of likelihood functions and posterior distributions. Further, they make numerical maximization and integration procedures easier to apply. Several applications are studied.
A generalized predictive criterion for model selection
Authors: Trottini Mario , Spezzaferri Fulvio 
Published: June 2006

AbstractGiven a random sample from some unknown model belonging to a finite class of parametric models, assume that the estimate of the density of a future observation is of interest San Martini & Spezzaferri (1984) proposed for this problem a predictive criterion based on the logarithmic utility function. The present authors investigate a generalization of this criterion that uses as a loss function an element of the class of α‐divergences discussed by Ali & Silvey (1966) and Csiszár (1967). They also discuss briefly the case in which the class of models considered is not exhaustive.
Worldwide research output in probability and statistics: An update
Authors: Genest Christian , Guay Mireille 
Published: June 2006

AbstractThe authors update the work of Genest (1997, 1999) on world research output in probability and statistics. The rankings they produce of countries and institutions are based on a survey of papers published between 1986 and 2000 in 25 specialized journals of high reputation in these two fields. The contribution of Canadian probabilists and statisticians is highlighted.
The estimating function bootstrap
Authors: Hu Feifang , Kalbfleisch John D. 
Published: June 2006

AbstractThe authors propose a bootstrap procedure which estimates the distribution of an estimating function by resampling its terms using bootstrap techniques. Studentized versions of this so‐called estimating function (EF) bootstrap yield methods which are invariant under reparametrizations. This approach often has substantial advantage, both in computation and accuracy, over more traditional bootstrap methods and it applies to a wide class of practical problems where the data are independent but not necessarily identically distributed. The methods allow for simultaneous estimation of vector parameters and their components. The authors use simulations to compare the EF bootstrap with competing methods in several examples including the common means problem and nonlinear regression. They also prove symptotic results showing that the studentized EF bootstrap yields higher order approximations for the whole vector parameter in a wide class of problems.
Likelihood inference for small variance components
Authors: Stern Steven E. , Welsh A. H. 
Published: June 2006

AbstractThe authors explore likelihood‐based methods for making inferences about the components of variance in a general normal mixed linear model. In particular, they use local asymptotic approximations to construct confidence intervals for the components of variance when the components are close to the boundary of the parameter space. In the process, they explore the question of how to profile the restricted likelihood (REML). Also, they show that general REML estimates are less likely to fall on the boundary of the parameter space than maximum‐likelihood estimates and that the likelihood‐ratio test based on the local asymptotic approximation has higher power than the likelihood‐ratio test based on the usual chi‐squared approximation. They examine the finite‐sample properties of the proposed intervals by means of a simulation study.
Conjugate analysis of multivariate normal data with incomplete observations
Authors: Dominici Francesca , Parmigiani Giovanni , Clyde Merlise 
Published: June 2006

AbstractThe authors discuss prior distributions that are conjugate to the multivariate normal likelihood when some of the observations are incomplete. They present a general class of priors for incorporating information about unidentified parameters in the covariance matrix. They analyze the special case of monotone patterns of missing data, providing an explicit recursive form for the posterior distribution resulting from a conjugate prior distribution. They develop an importance sampling and a Gibbs sampling approach to sample from a general posterior distribution and compare the two methods.
Kendall's tau for serial dependence
Authors: Ferguson Thomas S. , Genest Christian , Hallin Marc 
Published: June 2006

AbstractThe authors show how Kendall's tau can be adapted to test against serial dependence in a univariate time series context. They provide formulas for the mean and variance of circular and noncircular versions of this statistic, and they prove its asymptotic normality under the hypothesis of independence. They present also a Monte Carlo study comparing the power and size of a test based on Kendall's tau with the power and size of competing procedures based on alternative parametric and nonparametric measures of serial dependence. In particular, their simulations indicate that Kendall's tau outperforms Spearman's rho in detecting first‐order autoregressive dependence, despite the fact that these two statistics are asymptotically equivalent under the null hypothesis, as well as under local alternatives.
Geometric ergodicity of nonlinear autoregressive models with changing conditional variances
Authors: Chen Min , Chen Gemai 
Published: June 2006

AbstractThe authors give easy‐to‐check sufficient conditions for the geometric ergodicity and the finiteness of the moments of a random processxt= ϕ(xt‐1,…,xt‐p) + ϵtσ(xt‐1,…,xt‐q) in which ϕ: Rp→ R, σ Rq→ R and (ϵt) is a sequence of independent and identically distributed random variables. They deduce strong mixing properties for this class of nonlinear autoregressive models with changing conditional variances which includes, among others, the ARCH(p), the AR(p)‐ARCH(p), and the double‐threshold autoregressive models.
Nonparametric estimating equations based on a penalized information criterion
Authors: Li Bing 
Published: June 2006

AbstractIt has recently been observed that, given the mean‐variance relation, one can improve on the accuracy of the quasi‐likelihood estimator by the adaptive estimator based on the estimation of the higher moments. The estimation of such moments is usually unstable, however, and consequently only for large samples does the improvement become evident. The author proposes a nonparametric estimating equation that does not depend on the estimation of such moments, but instead on the penalized minimization of asymptotic variance. His method provides a strong improvement over the quasi‐likelihood estimator and the adaptive estimators, for a wide range of sample sizes.