bluuebunny/crossref_metadata_2025 huggingface dataset:
Nonparametric density estimation for censored survival data: Regression‐spline approach
Authors: Abrahamowicz Michal , Clampl Antonio , Ramsay James O.
Published: June 2006

A method for nonparametric estimation of density based on a randomly censored sample is presented. The density is expressed as a linear combination of cubicM‐splines, and the coefficients are determined by pseudo‐maximum‐likelihood estimation (likelihood is maximized conditionally on data‐dependent knots). By using regression splines (small number of knots) it is possible to reduce the estimation problem to a space of low dimension while preserving flexibility, thus striking a compromise between parametric approaches and ordinary nonparametric approaches based on spline smoothing. The number of knots is determined by the minimum AIC. Examples of simulated and real data are presented. Asymptotic theory and the bootstrap indicate that the precision and the accuracy of the estimates are satisfactory.
Beyond kappa: A review of interrater agreement measures
Authors: Banerjee Mousumi , Capozzoli Michelle , McSweeney Laura , Sinha Debajyoti
Published: June 2006

In 1960, Cohen introduced the kappa coefficient to measure chance‐corrected nominal scale agreement between two raters. Since then, numerous extensions and generalizations of this interrater agreement measure have been proposed in the literature. This paper reviews and critiques various approaches to the study of interrater agreement, for which the relevant data comprise either nominal or ordinal categorical ratings from multiple raters. It presents a comprehensive compilation of the main statistical approaches to this problem, descriptions and characterizations of the underlying models, and discussions of related statistical methodologies for estimation and confidence‐interval construction. The emphasis is on various practical scenarios and designs that underlie the development of these measures, and the interrelationships between them.
Smoothing in an underdetermined linear model with random explanatory variables
Authors: Sneddon Gary
Published: June 2006

In some physical systems, where the goal is to describe behaviour over an entire field using scattered observations, a multiple regression model can be derived from the discretization of a continuous process. These models often have more parameters than observations. We propose a technique for constructing smoothed estimators in this situation. Our method assumes the model has random explanatory and response variables, and imposes a smoothness penalty based on the signal‐to‐noise ratio of the model. Results are présentés using a known value for the ratio, and a method for estimating the ratio is discussed. The procedure is applied to modelling temperature measurements taken in the California Current.
Reference priors for a product of normal means when variances are unknown
Authors: Sun Dongchu , Ye Keying
Published: June 2006

The reference priors of Berger and Bernardo (1992) are derived for normal populations with unknown variances when the product of means is of interest. The priors are also shown to be Tibshirani's (1989) matching priors.
Bayesian density estimation using bernstein polynomials
Authors: Petrone Sonia
Published: June 2006

We propose a Bayesian nonparametric procedure for density estimation, for data in a closed, bounded interval, say [0,1]. To this aim, we use a prior based on Bemstein polynomials. This corresponds to expressing the density of the data as a mixture of given beta densities, with random weights and a random number of components. The density estimate is then obtained as the corresponding predictive density function. Comparison with classical and Bayesian kernel estimates is provided. The proposed procedure is illustrated in an example; an MCMC algorithm for approximating the estimate is also discussed.
Robust estimation of extremes
Authors: Dupuis D. J. , Field C. A.
Published: June 2006

We consider the problem of making inferences about extreme values from a sample. The underlying model distribution is the generalized extreme‐value (GEV) distribution, and our interest is in estimating the parameters and quantiles of the distribution robustly. In doing this we find estimates for the GEV parameters based on that part of the data which is well fitted by a GEV distribution. The robust procedure will assign weights between 0 and 1 to each data point. A weight near 0 indicates that the data point is not well modelled by the GEV distribution which fits the points with weights at or near 1. On the basis of these weights we are able to assess the validity of a GEV model for our data. It is important that the observations with low weights be carefully assessed to determine whether diey are valid observations or not. If they are, we must examine whether our data could be generated by a mixture of GEV distributions or whether some other process is involved in generating the data. This process will require careful consideration of die subject matter area which led to the data. The robust estimation techniques are based on optimal B‐robust estimates. Their performance is compared to the probability‐weighted moment estimates of Hoskinget al.(1985) in both simulated and real data.
On the trimmed mean and minimax‐variance L‐estimation in Kolmogorov neighbourhoods
Authors: Wiens Douglas P. , Wu Eden K.H. , Zhou Julie
Published: June 2006

We consider the properties of the trimmed mean, as regards minimax‐variance L‐estimation of a location parameter in a Kolmogorov neighbourhood K() of the normal distribution:

We first review some results on the search for an L‐minimax estimator in this neighbourhood, i.e. a linear combination of order statistics whose maximum variance in Kt() is a minimum in the class of L‐estimators. The natural candidate – the L‐estimate which is efficient for that member of Kt,() with minimum Fisher information – is known not to be a saddlepoint solution to the minimax problem. We show here that it is not a solution at all. We do this by showing that a smaller maximum variance is attained by an appropriately trimmed mean. We argue that this trimmed mean, as well as being computationally simple – much simpler than the efficient L‐estimate referred to above, and simpler than the minimax M‐ and R‐estimators – is at least “nearly” minimax.
Improved confidence estimators for Fieller's confidence sets
Authors: Tsao C. Andy , Hwang J. T. Gene
Published: June 2006

Fieller's confidence setCFfor ratios of location parameters, although of great importance in practice, is often cited as an example to criticize frequentist theory. The reason is that the set can consist of the whole parameter space and yet the confidence is γ = 1 – α in any case. In this paper, we study the problem of constructing data‐dependent estimators better than γ+, A reasonable estimator appears to be γ+, which is one ifCFis the whole parameter space and γ otherwise. By using an estimated confidence approach and a squared‐error loss, it is shown that γ+dominates γ. The risk improvement of γ+over γ can be sizable. Also, by numerically comparing γ+with a generalized Bayes estimator γL, which is shown to be admissible when one or two ratios are concerned, it is shown that γ+is nearly admissible. We also conclude that the common practice of reporting 1 – α only whenCFis not the whole parameter space is nearly admissible.
Bayesian analysis for a stress‐strength system under noninformative priors
Authors: Sun Dongchu , Ghosh Malay , Basu Asit P.
Published: June 2006

Noninformative priors are used for estimating the reliability of a stress‐strength system. Several reference priors (cf. Berger and Bernardo 1989, 1992) are derived. A class of priors is found by matching the coverage probabilities of one‐sided Bayesian credible intervals with the corresponding frequentist coverage probabilities. It turns out that none of the reference priors is a matching prior. Sufficient conditions for propriety of posteriors under reference priors and matching priors are provided. A simple matching prior is compared with three reference priors when sample sizes are small. The study shows that the matching prior performs better than Jeffreys's prior and reference priors in meeting the target coverage probabilities.
On the explosion rate of maximum‐bias functions
Authors: Berrendero José R. , Mazzi Sonia , Romo Juan , Zamar Ruben H.
Published: June 2006

The maxbias function BT() contains much information about the robustness properties of the estimate T. This function satisfies BT(0)=0 and BT()<for all 0<<whereis the breakdown point of T. Hampel (1974)pioneered the study of the limiting behaviour of BT(ϵ) where ϵ → 0. He computed and optimized the rate γ at which BT(ϵ) approaches 0 when ϵ → 0. This rate is now called the contamination sensitivity of T, and constitutes one of the cornerstones of the theory of robustness. We show that much can also be learned from the study of the limiting behaviour of BT(ϵ) when ϵ → ϵ*. A new robustness measure, called the relative explosion rate, can be obtained by studying the limiting relative maxbias behaviour of two extimates when approaches their common breakdown point ϵ*. Like the contamination sensitivity, the relative explosion rate can be readily derived from the estimate's score function. General formulae are given for M‐estimates of scale and S‐, MM‐ and τ‐estimates of regression. We also show that the maxbias behaviour for large ϵ is largely determined by the curvature of the estimate's score function near zero. This motivates our definition and study of the local order of a score function.
A generalized step‐up‐down multiple test procedure
Authors: Tamhane Ajit C. , Liu Wei , Dunnett Charles W.
Published: June 2006

A generalization of step‐up and step‐down multiple test procedures is proposed. This step‐up‐down procedure is useful when the objective is to reject a specified minimum number, q, out of a family of k hypotheses. If this basic objective is met at the first step, then it proceeds in a step‐down manner to see if more than q hypotheses can be rejected. Otherwise it proceeds in a step‐up manner to see if some number less than q hypotheses can be rejected. The usual step‐down procedure is the special case where q = 1, and the usual step‐up procedure is the special case where q = k. Analytical and numerical comparisons between the powers of the step‐up‐down procedures with different choices of q are made to see how these powers depend on the actual number of false hypotheses. Examples of application include comparing the efficacy of a treatment to a control for multiple endpoints and testing the sensitivity of a clinical trial for comparing the efficacy of a new treatment with a set of standard treatments.
Estimation of product moments of a stationary stochastic process with application to estimation of cumulants and cumulant spectral densities
Authors: Kim Peter T.
Published: June 2006

Inference concerning the structure of stationary stochastic processes can be investigated by looking at properties of various cumulant spectral densities of order two and higher. However, except for cases when cumulants and product moments are identical, estimation of higher‐order cumulant spectral densities has been restricted by the dependence of higher‐order cumulants on lower‐order product moments. By first estimating product moments and then using an identity between product moments and cumulants, asymptotically unbiased and consistent estimates of cumulants are obtained. This in turn leads to asymptotically unbiased and consistent estimators of higher‐order cumulant spectral densities. In addition, asymptotic normality of product‐moment estimators is exhibited under weak dependence.
Markov bridges and enlarged filtrations
Authors: Al‐Hussaini Ata N. , Elliott Robert J.
Published: June 2006

The semimartingale decomposition of a Markov chain, whose value at some future time is known, is obtained by considering an enlarged filtration.
Density estimation under the koziol‐green model of censoring by penalized likelihood methods
Authors: Gijbels I. , Klonias V. K.
Published: June 2006

We propose two density estimators of the survival distribution in the setting of the Koziol‐Green random‐censoring model. The estimators are obtained by maximum‐penalized‐likelihood methods, and we provide an algorithm for their numerical evaluation. We establish the strong consistency of the estimators in the Hellinger metric, the Lp‐norms, p= 1,2, ∞, and a Sobolev norm, under mild conditions on the underlying survival density and the censoring distribution.
Correlated linear models for the analysis of familial correlations
Authors: Shoukri M. M. , Mian I. U. H. , Tracy D. S.
Published: June 2006

The problems of estimation and hypotheses testing on the parameters of two correlated linear models are discussed. Such models are known to have direct applications in epidemiologic research, particularly in the field of family studies. When the data are unbalanced, the maximum‐likelihood estimation of the parameters is achieved by adopting a fairly simple numerical algorithm. The asymptotic variances and covariances of the estimators are derived, and the procedures are illustrated on arterial‐blood‐pressure data from the literature.
On the estimation of the influence curve
Authors: Cuevas Antonio , Romo Juan
Published: June 2006

We prove the asymptotic validity of bootstrap confidence bands for the influence curve from its usual estimator (the sensitivity curve). The proof is based on the use of Gill's generalized delta method for Hadamard differentiable operators. Some statistical applications, in particular to the estimation of asymptotic variance, are given.
The analysis of incomplete data using stochastic covariates
Authors: Rai S.N. , Matthews D.E.
Published: June 2006

In the development of many diseases there are often associated random variables which continuously reflect the progress of a subject towards the final expression of the disease (failure). At any given time these processes, which we call stochastic covariates, may provide information about the current hazard and the remaining time to failure. Likewise, in situations when the specific times of key prior events are not known, such as the time of onset of an occult tumour or the time of infection with HIV‐1, it may be possible to identify a stochastic covariate which reveals, indirectly, when the event of interest occurred. The analysis of carcinogenicity trials which involve occult tumours is usually based on the time of death or sacrifice and an indicator of tumour presence for each animal in the experiment. However, the size of an occult tumour observed at the endpoint represents data concerning tumour development which may convey additional information concerning both the tumour incidence rate and the rate of death to which tumour‐bearing animals are subject. We develop a stochastic model for tumour growth and suggest different ways in which the effect of this growth on the hazard of failure might be modelled. Using a combined model for tumour growth and additive competing risks of death, we show that if this tumour size information is used, assumptions concerning tumour lethality, the context of observation or multiple sacrifice times are no longer necessary in order to estimate the tumour incidence rate. Parametric estimation based on the method of maximum likelihood is outlined and is applied to simulated data from the combined model. The results of this limited study confirm that use of the stochastic covariate tumour size results in more precise estimation of the incidence rate for occult tumours.
Beer chemistry and canadians' beer preferences
Authors: Whitmore G. A. , Gentleman Jane F.
Published: June 2006

Beer companies want to understand the relationship between the chemical characteristics of beer and the preferences for beer exhibited by consumers. Two data sets were provided to the analysts in this case study. The first set consisted of chemical measurements on 91 beers and preference measurements on the same beers collected from beer consumers in blind taste tests. The analysts were asked to use these data to develop a statistical model relating beer chemistry and consumer preferences for beer. The second data set consisted of chemical measurements on a holdout sample of 37 beers. The analysts were asked to employ their statistical model to predict consumer preferences for the beers in the holdout sample. The case study assesses the success of their modelling efforts.
Assessing case influence on confidence intervals in nonlinear regression
Authors: Dzieciolowski Krzysztof , Ross William H.
Published: June 2006

Diagnostic techniques are proposed for assessing the influence of individual cases on confidence intervals in nonlinear regression. The technique proposed uses the method of profilet‐plots applied to the case‐deletion model. The effect of the geometry of the statistical model on the influence measures is assessed, and an algorithm for computing case‐deleted confidence intervals is described. This algorithm provides a direct method for constructing a simple diagnostic measure based on the ratio of the lengths of confidence intervals. The generalization of these methods to multiresponse models is discussed.
Hierarchical bayesian curve fitting and smoothing
Authors: Angers Jean‐François , Delampady Mohan
Published: June 2006

Estimation of a smooth function is considered when observations on this function added with Gaussian errors are observed. The problem is formulated as a general linear model, and a hierarchical Bayesian approach is then used to study it. Credible bands are also developed for the function. Sensitivity analysis is conducted to determine the influence of the choice of priors on hyperparameters. Finally, the methodology is illustrated using real and simulated examples where it is compared with classical cubic splines. It is also shown that our approach provides a Bayesian solution to some problems in discrete time series.
Orthogonalizing parametric link transformation families in binary regression analysis
Authors: Czado Claudia , Santner Thomas J.
Published: June 2006

This paper studies the application of the orthogonalization technique of Cox and Reid (1987) to parametric families of link functions used in binary regression analysis. The explicit form of Cox and Reid's condition (4), for orthogonality at a point, is derived for arbitrary link families. This condition is used to determine a transform of a family introduced by Burr (1942) and Prentice (1975, 1976) which is locally orthogonal when the regression parameter is zero. Thus the benefits of having orthogonal parameters are limited to “small” regression effects. The extent to which approximate orthogonality holds for nonzero regression coefficients is investigated for two data sets from the literature. Two specific issues considered are: (1) the ability of orthogonal reparametrization to reduce the variability of the regression parameters caused by estimation of the link parameter and (2) the improved numerical stability (and hence interpretability) of regression estimates corresponding to different link parameters.
Limit theorems for a general weighted process under random censoring
Authors: Einmahl John H.J. , Koning Alex J.
Published: June 2006

Necessary and sufficient conditions for weak and strong convergence are derived for the weighted version of a general process under random censoring. To be more explicit, this means that for this process complete analogues are obtained of the Chibisov‐O'Reilly theorem, the Lai‐Wellner Glivenko‐Cantelli theorem, and the James law of the iterated logarithm for the empirical process. The process contains as special cases the so‐called basic martingale, the empirical cumulative hazard process, and the product‐limit process. As a tool we derive a Kiefer‐process‐type approximation of our process, which may be of independent interest.
Time series, point processes, and hybrids
Authors: Brillinger David R.
Published: June 2006

Techniques developed for the study of time series, point processes, and marked point processes can suggest corresponding techniques for each other, and common techniques can be recognized. In this paper connections are drawn based on conceptual foundations, basic parameters, analyses, displays, algorithms, problems, models. The definitions and techniques are brought out by specific scientific problems. The emphasis is on the single‐realization stationary case and on the use of second‐ and third‐order moments to help understand the realization. The tool of stacking, at a particular period, is employed in several of the examples.
Binary‐image restoration
Authors: Meloche J. , Zamar R.H.
Published: June 2006

We consider the problem of binary‐image restoration. The image being restored is not random, and we make no assumption about the nature of its contents. The estimate of the colour at each site is a fixed (the same for all sites) function of the data available in a neighbourhood of that site. Under this restriction, the estimate minimizing the overall mean squared error of prediction is the conditional expectation of the true colour given the observations in the neighbourhood of a site. The computation of this conditional expectation leads to the formal definition of the local characteristics of an image, namely, the frequency with which each pattern appears in the true unobserved image. When the “true” distribution of the patterns is unknown, it can be estimated from the records. The conditional expectation described above can then be evaluated using the estimated distribution of the patterns, and this procedure leads to a very natural estimate of the colour at each site. We propose two unbiased and consistent estimates for the distribution of patterns when the noise is a Gaussian white noise. Since the size of realistic images is very large, the estimated pattern distribution is usually close to the true one. This suggests that the estimated conditional expectation can be expected to be nearly optimal. An interesting feature of the proposed restoration methods is that they do not require prior knowledge of the local or global properties of the true underlying image. Several examples based on synthetic images show that the new methods perform fairly well for a variety of images with different degrees of colour continuity or textures.
Nonparametric Bayes methods for directional data
Authors: Brunner Lawrence J. , Lo Albert Y.
Published: June 2006

A model for directional data in q dimensions is studied. The data are assumed to arise from a distribution with a density on a sphere of q — 1 dimensions. The density is unimodal and rotationally symmetric, but otherwise of unknown form. The posterior distribution of the unknown mode (mean direction) is derived, and small‐sample posterior inference is discussed. The posterior mean of the density is also given. A numerical method for evaluating posterior quantities based on sampling a Markov chain is introduced. This method is generally applicable to problems involving unknown monotone functions.
Graphical methods for ranking data
Authors: Alvo Mayer , Ertas Kadir
Published: June 2006

Graphical methods are presented for the analysis of ranking data collected from g groups of rankers. The data provided by a single individual consist of the ranks of r objects. The sample space is the space of all permutations and has cardinality r! In order to reduce the dimensionality of the data and to study the interrelationships among rankers and items, a two‐stage approach is proposed. First, transformations motivated by various metrics on permutations are defined. In particular, the Kendall metric gives rise to pairwise comparisons. Then, the transformed data are analyzed using results in connection with the generalized singular‐value decomposition of a matrix. The methods are illustrated on two examples.
Likelihood and higher‐order approximations to tail areas: A review and annotated bibliography
Authors: Reid N.
Published: June 2006

Recent developments in higher‐order asymptotic theory for statistical inference have emphasized the fundamental role of the likelihood function in providing accurate approximations to cumulative distribution functions. This paper summarizes the main results, with an emphasis on classes of problems for which relatively easily implemented solutions exist. A survey of the literature indicates the large number of problems solved and solvable by this method. Generalizations and extensions, with suggestions for further development, are considered.
Estimation of regression parameters in generalized linear models for cluster correlated data with measurement error
Authors: Sutradhar B.C. , Rao J.N.K.
Published: June 2006

Liang and Zeger (1986) introduced a class of estimating equations that gives consistent estimates of regression parameters and of their asymptotic variances in the class of generalized linear models for cluster correlated data. When the independent variables or covariates in such models are subject to measurement errors, the parameter estimates obtained from these estimating equations are no longer consistent. To correct for the effect of measurement errors, an estimator with smaller asymptotic bias is constructed along the lines of Stefanski (1985), assuming that the measurement error variance is either known or estimable. The asymptotic distribution of the bias‐corrected estimator and a consistent estimator of its asymptotic variance are also given. The special case of a binary logistic regression model is studied in detail. For this case, methods based on conditional scores and quasilikelihood are also extended to cluster correlated data. Results of a small simulation study on the performance of the proposed estimators and associated tests of hypotheses are reported.
Nonhomogeneous poisson processes as overhaul models
Authors: Dykstra R.L. , Barmi Hammou El , Guffey James M. , Wright F.T.
Published: June 2006

Hollander and Proschan (1974) studied nonhomogeneous Poisson processes as models for systems subject to overhauls. They did not postulate a functional form for the intensity, but showed that certain basic assumptions about the deterioration of the system implied that the mean function is superadditive. They studied tests of the null hypothesis that the intensity is constant with the alternative restricted to superadditive mean functions. For estimation purposes, the class of superadditive mean functions is too broad. We assume that the intensity is nondecreasing between overhauls and that at an overhaul it does not fall below its average prior to the overhaul. These two assumptions imply that the mean function is star‐shaped. We obtain the restricted maximum‐likelihood estimates under these two assumptions and under the star‐shaped restriction. The two estimates are compared on a data set.
The weighted sequential likelihood ratio
Authors: Gombay Edit
Published: June 2006

Strong approximation of the maximum‐likelihood‐ratio statistic by a diffusion process is given. This allows one to develop statistics using different weight functions. Sequential tests obtained include the ones earlier defined by Barbour (1979). The precision of the approximations is examined.
Characterization theorems for some discrete distributions based on conditional structure
Authors: Wang Y. , Gupta A.K. , Nguyen T.T.
Published: June 2006

The joint distribution of (X,Y) is determined if the conditional expectationE{g(X)|Y=y} is given and the conditional distribution ofY|(X=x) is a conditional power series distribution, whereg(·) is a function satisfying some minor conditions.
Higher‐order asymptotics under model misspecification
Authors: Viraswami K. , Reid N.
Published: June 2006

Most of the higher‐order asymptotic results in statistical inference available in the literature assume model correctness. The aim of this paper is to develop higher‐order results under model misspecification. The density functions to O(n−3/2) of the robust score test statistic and the robust Wald test statistic are derived under the null hypothesis, for the scalar as well as the multiparameter case. Alternate statistics which are robust to O(n−3/2) are also proposed.
A full Bayesian analysis of circular data using the von Mises distribution
Authors: Damien Paul , Walker Stephen
Published: June 2006

This paper presents a full Bayesian analysis of circular data, paying special attention to the von Mises distribution. We obtain samples from the posterior distribution using the Gibbs sampler which, after the introduction of strategic latent variables, has all full conditional distributions of known type.
A geometric optimally of Cox's partial likelihood
Authors: Chan Schultz , Ghosh Malay
Published: June 2006

The paper proves geometric optimality of Cox's partial likelihood score functions via estimating functions. As an illustration, Cox's proportional‐hazards model is considered.

Les auteurs démontrent l'optimalité gǵométrique des fonctions scores de vraisemblance partielle de Cox au moyen des fonctions d'estimation. Le modéle des risques proportionnels de Cox permet d'illustrer leur résultat.
An invariance principle for triangular arrays of dependent variables with application to autocovariance estimation
Authors: Chen Hui , Romano Joseph P.
Published: June 2006

The invariance principle for triangular arrays of dependent variables is studied. We use the concept of mixingale, proposed by McLeish (1975). Uniform bounds are imposed on the growth of conditional expectations with respect to distant predecessors. The theorem is applied to invariance principles for autocovariance estimates based on triangular arrays of time‐series data for weak mixing sequences and linear processes. Such results are required for bootstrap applications.
The optimal prediction of cross‐sectional proportions in categorical panel‐data analysis
Authors: Zhang Ping
Published: June 2006

Longitudinal study is a powerful tool in many areas of empirical research, including healthcare research, environmental monitoring and econometrics. In econometrics, the data generated through longitudinal studies are often referred to as panel data. Such data combine the features of both cross‐sectional and time‐series measurements. However, the vast literature on panel‐data analysis focuses almost exclusively on the treatment of cross‐sectional heterogeneity. Few studies address the problem of modeling panel data from a prediction point of view. In this article, we first formulate the prediction problem for categorical panel data. We then argue that prediction methods that are natural for other types of data may not be appropriate for panel data. Our main result shows that the optimal predictor, among a broad class of consistent predictors, is equivalent to a nonrandomized classification procedure that is determined by a set of integral equations.

Le recours é des enquětes longitudinales est fréquent et souvent trés profitable dans des disciplines expérimentales comme les sciences de la santé, les sciences de l'environnement ou I'économétrie. Dans ce dernier domaine, ce type d'enquěte donne lieu á des données dites de panel, qui component á la fois une composante transversale et une composante chronologique. Les nombreux écrits sur le sujet concernent pour la plupart le traitement de l'hétérogénéité transversale. Rares sont les études qui s'attaquent au probléme de la modélisation et de la prévision de ce genre de données. L'auteur commence done par formuler le probléme de la prévision á partir de données de panel catégoriques. II soutient ensuite que certaines méthodes de prévision qui sont naturelles pour d'autres types de données ne conviennent pas forcément dans ce contexte. Son résultat principal est á l'effet que I'élemént qui est optimal au sein d'une large classe de prédicteurs convergents est en fait équivalent á une procédure de classification non aléatoire qui est solution d'un ensemble d'équations intégrates.
Order‐restricted hypothesis testing in a variation of the normal mixture model
Authors: Nettleton Dan
Published: June 2006

This paper examines likelihood‐ratio tests concerning the relationships among a fixed number of univariate normal means given a sample of normal observations whose population membership is uncertain. The asymptotic null distributions of likelihood‐ratio test statistics are derived for a class of tests including hypotheses which place linear inequality constraints on the normal means. The use of such tests in the interval mapping of quantitative trait loci is addressed.
Confidence estimation of a normal mean vector with incomplete data
Authors: Krishnamoorthy K. , Pannala Maruthy K.
Published: June 2006

The problem of confidence estimation of a normal mean vector when data on different subsets of response variables are missing is considered. A simple approximate confidence region is proposed when the data matrix is of monotone pattern. Simultaneous inferential procedures based on Scheffe's method and Bonferroni's method are outlined. Further, applications of the results to a repeated measurements model are given. The results are illustrated using a practical example.
Joint estimation of the mean and dispersion parameters in the analysis of proportions: A comparison of efficiency and bias
Authors: Paul S. R. , Islam A. S.
Published: June 2006

This paper deals with joint estimation of the mean and dispersion parameters in the analysis of proportions. We consider a parametric model, namely the extended beta‐binomial model, and several semiparametric procedures. We study large‐sample efficiency and small‐sample bias and efficiency properties of the estimates of the mean and intraclass correlation parameters. Estimation and efficiency calculations are présentés for the regression model. However, for simplicity, numerical large‐sample efficiency and small‐sample bias and efficiency calculations are performed for the two‐parameter model only. Numerical efficiency results are présentés in terms of graphs. Estimated asymptotic efficiencies of various estimates are also compared for two data sets. Our findings suggest that for the estimation of the mean (regression) parameters the quasilikelihood procedure performs best. However, for the joint estimation, the Gaussian likelihood estimates perform best.
Hidden Markov chains in generalized linear models
Authors: Turner T. Rolf , Cameron Murray A. , Thomson Peter J.
Published: June 2006

We show how the concept of hidden Markov model may be accommodated in a setting involving multiple sequences of observations. The resulting class of models allows for both interrelationships between different sequences and serial dependence within sequences. Missing values in the observation sequences may be handled in a straightforward manner. We also examine a group of methods, based upon the observed Fisher Information matrix, for estimating the covariance matrix of the parameter estimates. We illustrate the methods with both real and simulated data sets.
On approximate likelihood inference in a poisson mixed model
Authors: Sutradhar Brajendra C. , Qu Zhende
Published: June 2006

A 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

Consider 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

We 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

Due 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

We 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

We 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

Recently, 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

This 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

Very 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

We 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

Magnetized 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

Elephant 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

We 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

By 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

This 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.