bluuebunny/crossref_metadata_2025_split huggingface dataset:
Alternative Bayes factors for model selection
Authors: De Santis Fulvio , Spezzaferri Fulvio 
Published: June 2006

AbstractSeveral alternative Bayes factors have been recently proposed in order to solve the problem of the extreme sensitivity of the Bayes factor to the priors of models under comparison. Specifically, the impossibility of using the Bayes factor with standard noninformative priors for model comparison has led to the introduction of new automatic criteria, such as the posterior Bayes factor (Aitkin 1991), the intrinsic Bayes factors (Berger and Pericchi 1996b) and the fractional Bayes factor (O'Hagan 1995). We derive some interesting properties of the fractional Bayes factor that provide justifications for its use additional to the ones given by O'Hagan. We further argue that the use of the fractional Bayes factor, originally introduced to cope with improper priors, is also useful in a robust analysis. Finally, using usual classes of priors, we compare several alternative Bayes factors for the problem of testing the point null hypothesis in the univariate normal model.
Overdispersed poisson regression models for studies of air pollution and human health
Authors: McNeney Brad , Petkau John 
Published: June 2006

AbstractThis paper presents results from a simulation study motivated by a recent study of the relationships between ambient levels of air pollution and human health in the community of Prince George, British Columbia. The simulation study was designed to evaluate the performance of methods based on overdispersed Poisson regression models for the analysis of series of count data. Aspects addressed include estimation of the dispersion parameter, estimation of regression coefficients and their standard errors, and the performance of model selection tests. The effects of varying amounts of overdispersion and differing underlying variance structure on this performance were of particular interest. This study is related to work reported by Breslow (1990) although the context is quite different. Preliminary work led to the conclusion that estimation of the dispersion parameter should be based on Pearson's chi‐square statistic rather than the Poisson deviance. Regression coefficients are well estimated, even in the présence of substantial overdispersion and when the model for the variance function is incorrectly specified. Despite potential greater variability, the empirical estimator of the covariance matrix is preferred because the model‐based estimator is unreliable in general. When the model for the variance function is incorrect, model‐based test statistics may perform poorly, in sharp contrast to empirical test statistics, which performed very well in this study.
Multivariate spatial interpolation and exposure to air pollutants
Authors: Brown Philip J. , Le Nhu D. , Zidek James V. 
Published: June 2006

AbstractWe develop and apply an approach to the spatial interpolation of a vector‐valued random response field. The Bayesian approach we adopt enables uncertainty about the underlying models to be représentés in expressing the accuracy of the resulting interpolants. The methodology is particularly relevant in environmetrics, where vector‐valued responses are only observed at designated sites at successive time points. The theory allows space‐time modelling at the second level of the hierarchical prior model so that uncertainty about the model parameters has been fully expressed at the first level. In this way, we avoid unduly optimistic estimates of inferential accuracy. Moreover, the prior model can be upgraded with any available new data, while past data can be used in a systematic way to fit model parameters. The theory is based on the multivariate normal and related joint distributions. Our hierarchical prior models lead to posterior distributions which are robust with respect to the choice of the prior (hyperparameters). We illustrate our theory with an example involving monitoring stations in southern Ontario, where monthly average levels of ozone, sulphate, and nitrate are available and between‐station response triplets are interpolated. In this example we use a recently developed method for interpolating spatial correlation fields.
Small‐area estimation by combining time‐series and cross‐sectional data
Authors: Rao J. N. K. , Yu Mingyu 
Published: June 2006

AbstractA model involving autocorrelated random effects and sampling errors is proposed for small‐area estimation, using both time‐series and cross‐sectional data. The sampling errors are assumed to have a known block‐diagonal covariance matrix. This model is an extension of a well‐known model, due to Fay and Herriot (1979), for cross‐sectional data. A two‐stage estimator of a small‐area mean for the current period is obtained under the proposed model with known autocorrelation, by first deriving the best linear unbiased prediction estimator assuming known variance components, and then replacing them with their consistent estimators. Extending the approach of Prasad and Rao (1986, 1990) for the Fay‐Herriot model, an estimator of mean squared error (MSE) of the two‐stage estimator, correct to a second‐order approximation for a small or moderate number of time points, T, and a large number of small areas, m, is obtained. The case of unknown autocorrelation is also considered. Limited simulation results on the efficiency of two‐stage estimators and the accuracy of the proposed estimator of MSE are présentés.
Testing for and against a set of linear inequality constraints in a multinomial setting
Authors: Barmi Hammou El , Dykstra Richard 
Published: June 2006

AbstractThere are numerous situations in categorical data analysis where one wishes to test hypotheses involving a set of linear inequality constraints placed upon the cell probabilities. For example, it may be of interest to test for symmetry in k × k contingency tables against one‐sided alternatives. In this case, the null hypothesis imposes a set of linear equalities on the cell probabilities (namely pij = Pji ×i > j), whereas the alternative specifies directional inequalities. Another important application (Robertson, Wright, and Dykstra 1988) is testing for or against stochastic ordering between the marginals of a k × k contingency table when the variables are ordinal and independence holds. Here we extend existing likelihood‐ratio results to cover more general situations. To be specific, we consider testing Ht,0 against H1 ‐ H0 and H1 against H2 ‐ H 1 when H0:k × i=1 pixji = 0, j = 1,…, s, H1:k × i=1 pixji × 0, j = 1,…, s, and does not impose any restrictions on p. The xji's are known constants, and s × k ‐ 1. We show that the asymptotic distributions of the likelihood‐ratio tests are of chi‐bar‐square type, and provide expressions for the weighting values.
Comparing three bootstrap methods for survey data
Authors: Sitter R. R. 
Published: June 2006

AbstractVarious bootstrap methods for variance estimation and confidence intervals in complex survey data, where sampling is done without replacement, have been proposed in the literature. The oldest, and perhaps the most intuitively appealing, is the without‐replacement bootstrap (BWO) method proposed by Gross (1980). Unfortunately, the BWO method is only applicable to very simple sampling situations. We first introduce extensions of the BWO method to more complex sampling designs. The performance of the BWO and two other bootstrap methods, the rescaling bootstrap (Rao and Wu 1988) and the mirror‐match bootstrap (Sitter 1992), are then compared through a simulation study. Together these three methods encompass the various bootstrap proposals.
On a problem of counting by weighing
Authors: Yu Kai Fun 
Published: June 2006

AbstractSuppose it is desired to obtain a large number Ns of items for which individual counting is impractical, but one can demand a batch to weigh at least w units so that the number of items N in the batch may be close to the desired number Ns. If the items have mean weight ωTH, it is reasonable to have w equal to ωTHNs when ωTH is known. When ωTH is unknown, one can take a sample of size n, not bigger than Ns, estimate ωTH by a good estimator ωn, and set w equal to ωnNs. Let Rn = Kp2N2s/n + Ksn be a measure of loss, where Ke and Ks are the coefficients representing the cost of the error in estimation and the cost of the sampling respectively, and p is the coefficient of variation for the weight of the items. If one determines the sample size to be the integer closest to pCNs when p is known, where C is (Ke/Ks)1/2, then Rn will be minimized. If p is unknown, a simple sequential procedure is proposed for which the average sample number is shown to be asymptotically equal to the optimal fixed sample size. When the weights are assumed to have a gamma distribution given ω and ω has a prior inverted gamma distribution, the optimal sample size can be found to be the nonnegative integer closest to pCNs + p2A(pC – 1), where A is a known constant given in the prior distribution.
Sequential sampling without recall from a dirichlet process
Authors: Christensen Ronald 
Published: June 2006

AbstractThe problem of sequential sampling without recall from a Dirichlet process is studied. An individual observes a sequential samplep1,p2, … . At each stage the observer can either accept the current valuepior continue sampling. The total cost to the observer is the current value plus a cost for each observation taken after the first. A concrete context for the problem is provided by a shopper who must buy a particular item and can elicit price quotations sequentially but must pay for each quotation. Qualitative properties of optimal search rules are derived which establish that the problem is well behaved. In particular, the reservation‐price property is shown to hold. The results extend those in Christensen (1986).
Empirical bayes estimation of reliability characteristics for an exponential family
Authors: Pensky M. , Singh R. S. 
Published: June 2006

AbstractThis paper considers empirical Bayes (EB) squared‐error‐loss estimations of mean lifetime, variance and reliability function for failure‐time distributions belonging to an exponential family, which includes gamma and Weibull distributions as special cases. EB estimators are proposed when the prior distribution of the lifetime parameter is completely unknown but has a compact (known or unknown) support. Asymptotic optimality and rates of convergence of these estimators are investigated. The rates established here under the compact support restriction are better than the polynomial rates of convergence obtained previously.
A uniform saddlepoint expansion for the null‐distribution of the wilcoxon‐mann‐whitney statistic
Authors: Froda Sorana , Van Eeden Constance 
Published: June 2006

AbstractThe authors give the exact coefficient of 1/Nin a saddlepoint approximation to the Wilcoxon‐Mann‐Whitney null‐distribution. This saddlepoint approximation is obtained from an Edgeworth approximation to the exponentially tilted distribution. Moreover, the rate of convergence of the relative error is uniformly of orderO(1/N) in a large deviation interval as defined in Feller (1971). The proposed method for computing the coefficient of 1/Ncan be used to obtain the exact coefficients of 1/Ni, for anyi. The exact formulas for the cumulant generating function and the cumulants, needed for these results, are those of van Dantzig (1947‐1950).
The run length distributions of the R, s and s2 control charts when is estimated
Authors: Chen Gemai 
Published: June 2006

AbstractR, s and s2 charts with estimated control limits are widely used in practice. Common practice in control‐chart theory is to estimate the control limits using data from the process and, once the process is determined to be in control, to treat the resulting control limits as though fixed. While there are empirical rules for setting up the control charts using past or trial data, little is known about the run length distributions of these charts when the fact that control limits are estimated is taken into account. In this paper, we derive and evaluate the run length distributions associated with the R, s and s2 charts when the process standard deviation a is estimated. The results are then used to discuss the appropriateness of the widely followed empirical rules for choosing the number m of samples and the sample size n.
A Bayesian approach to some overdispersion models
Authors: Albert James H. , Pepple Patricia A. 
Published: June 2006

AbstractIn fitting a generalized linear model, many authors have noticed that data sets can show greater residual variability than predicted under the exponential family. Two main approaches have been used to model this overdispersion. The first approach uses a sampling density which is a conjugate mixture of exponential family distributions. The second uses a quasilikelihood which adds a new scale parameter to the exponential likelihood. The approaches are compared by means of a Bayesian analysis using noninformative priors. In examples, it is indicated that the posterior analysis can be significantly different using the two approaches.
On the choice of optimality criteria in comparing statistical designs
Authors: Shah K. R. , Sinha B. K. 
Published: June 2006

AbstractWe formulate in a reasonable sense a class of optimality functionals for comparing feasible statistical designs available in a given setup. It is desired that the optimality functionals reflect symmetric measures of the lack of information contained in the designs being compared. In view of this, Kiefer's (1975) universal optimality criterion is seen to rest on stringent conditions, some of which can be relaxed while preserving optimality (in an extended sense) of the so‐calledbalanceddesigns.
On the asymptotic normality of functions of uniform spacings
Authors: Beirlant J. , Janssen P. , Veraverbeke N. 
Published: June 2006

AbstractA new proof is given for the asymptotic normality of sum functions of spacings, providing an alternative to the method of Le Cam (1958). The result is obtained under an optimal moment condition. The proof is based on a simple decomposition into a leading term, which is asymptotically normal, and a remainder term, which is shown to be negligible.
Testing independence with additional information
Authors: Perron François 
Published: June 2006

AbstractLet X = (Xj : j = 1,…, n) be n row vectors of dimension p independently and identically distributed multinomial. For each j, Xj is partitioned as Xj = (Xj1, Xj2, Xj3), where pi is the dimension of Xji with p1 = 1,p1+p2+p3 = p. In addition, consider vectors Yji, i = 1,2j = 1,…,ni that are independent and distributed as X1i. We treat here the problem of testing independence between X11 and X13 knowing that X11 and X12 are uncorrected. A locally best invariant test is proposed for this problem.
A multivariate Wald‐Wolfowitz rank test against serial dependence
Authors: Hallin Marc , Puri Madan L. 
Published: June 2006

AbstractRank‐based cross‐covariance matrices, extending to the case of multivariate observed series the (univariate) rank autocorrelation coefficients introduced by Wald and Wolfowitz (1943), are considered. A permutational central limit theorem is established for the joint distribution of such matrices, under the null hypothesis of (multivariate) randomness as well as under contiguous alternatives of (multivariate) ARMA dependence. A rank‐based, permutationaily distribution‐free test of the portmanteau type is derived, and its asymptotic local power is investigated. Finally, a modified rank‐based version of Tiao and Box's model specification procedure is proposed, which is likely to be more reliable under non‐Gaussian conditions, and more robust against gross errors.RÉSUMÉDes matrices de covariances croisées fondées sur les rangs, généralisant au cas des séries multivariées les coefficients d'autocorrélation de rangs introduits par Wald et Wolfowitz (1943) sont considérées. Un théorème central‐limite permutationnel est établi pour ces matrices, sous Phypothèse que la sérle sous‐jacente constitue la réalisation d'un bruit blanc multivarié, ainsi que sous des contre‐hypothèses contiguës de dépendance ARMA. Un test de rangs du type portemanteau est également construit, et sa puissance asymptotique locale est explicitement calculée. Enfin, une version fondée sur les rangs de la procédure d'identification de Tiao et Box est proposée. Celle‐ci est plus fiable que la procédure usuelle sous des conditions non gaussiennes, et plus robuste par rapport à la présence de valeurs aberrantes.
Computationally efficient classes of higher‐order kernel functions
Authors: Abdous Belkacem 
Published: June 2006

AbstractClasses of higher‐order kernels for estimation of a probability density are constructed by iterating the twicing procedure. Given a kernelKof orderl, we build a family of kernelsKmof ordersl(m+ 1) with the attractive property that their Fourier transforms are simply 1 — {1 —$(.)}m+1, where Ǩ is the Fourier transform ofK. These families of higher‐order kernels are well suited when the fast Fourier transform is used to speed up the calculation of the kernel estimate or the least‐squares cross‐validation procedure for selection of the window width. We also compare the theoretical performance of the optimal polynomial‐based kernels with that of the iterative twicing kernels constructed from some popular second‐order kernels.
Robust methods for personal‐income distribution models
Authors: Victoria‐Feser Maria‐Pia , Ronchetti Elvezio 
Published: June 2006

AbstractStatistical problems in modelling personal‐income distributions include estimation procedures, testing, and model choice. Typically, the parameters of a given model are estimated by classical procedures such as maximum‐likelihood and least‐squares estimators. Unfortunately, the classical methods are very sensitive to model deviations such as gross errors in the data, grouping effects, or model misspecifications. These deviations can ruin the values of the estimators and inequality measures and can produce false information about the distribution of the personal income in a country. In this paper we discuss the use of robust techniques for the estimation of income distributions. These methods behave like the classical procedures at the model but are less influenced by model deviations and can be applied to general estimation problems.
Generalized likelihood‐ratio test of the number of components in finite mixture models
Authors: Chen Jiahua 
Published: June 2006

AbstractThe number of components is an important feature in finite mixture models. Because of the irregularity of the parameter space, the log‐likelihood‐ratio statistic does not have a chi‐square limit distribution. It is very difficult to find a test with a specified significance level, and this is especially true for testing k — 1 versus k components. Most of the existing work has concentrated on finding a comparable approximation to the limit distribution of the log‐likelihood‐ratio statistic. In this paper, we use a statistic similar to the usual log likelihood ratio, but its null distribution is asymptotically normal. A simulation study indicates that the method has good power at detecting extra components. We also discuss how to improve the power of the test, and some simulations are performed.
A Bayesian method for classification and discrimination
Authors: Lavine Michael , West Mike 
Published: June 2006

AbstractWe discuss Bayesian analyses of traditional normal‐mixture models for classification and discrimination. The development involves application of an iterative resampling approach to Monte Carlo inference, commonly called Gibbs sampling, and demonstrates routine application. We stress the benefits of exact analyses over traditional classification and discrimination techniques, including the ease with which such analyses may be performed in a quite general setting, with possibly several normal‐mixture components having different covariance matrices, the computation of exact posterior classification probabilities for observed data and for future cases to be classified, and posterior distributions for these probabilities that allow for assessment of second‐level uncertainties in classification.
A counterexample to a conjecture on random shadows
Authors: Small Christopher G. 
Published: June 2006

AbstractWe construct a counterexample to a conjecture in stereology. It is well known that two convex solid bodies which cast congruent orthographic shadows on any common plane must necessarily be congruent to each other. This characterization fails if the orientations of the shadows are allowed to differ. Such counterexamples as have been constructed for the latter case fail to have the same distribution of random shadows projected onto planes with random orientation. Therefore P. McCullagh has conjectured that two bodies whose random shadows have the same distribution are necessarily congruent. We construct a counterexample to this conjecture. Some implications are drawn for the development of a general theory of stereological reconstruction based upon random projected shadows or images.
Ultrastructural elliptical models
Authors: Arellano‐Valle R.B. , Bolfarine H. , Vilca‐Labra F. 
Published: June 2006

AbstractDolby's (1976) ultrastructural model with no replications is investigated within the class of the elliptical distributions. General asymptotic results are given for the sample covariance matrixSin the presence of incidental parameters. These results are used to study the asymptotic behaviour of some estimators of the slope parameter, unifying and extending existing results in the literature. In particular, under some regularity conditions they are shown to be consistent and asymptotically normal. For the special case of the structural model, some asymptotic relative efficiencies are also reported which show that generalized least squares and the method of moment estimators can be highly inefficient under nonnormality.
Sequential importance sampling for nonparametric Bayes models: The next generation
Authors: Maceachern Steven N. , Clyde Merlise , Liu Jun S. 
Published: June 2006

AbstractThere are two generations of Gibbs sampling methods for semiparametric models involving the Dirichlet process. The first generation suffered from a severe drawback: the locations of the clusters, or groups of parameters, could essentially become fixed, moving only rarely. Two strategies that have been proposed to create the second generation of Gibbs samplers are integration and appending a second stage to the Gibbs sampler wherein the cluster locations are moved. We show that these same strategies are easily implemented for the sequential importance sampler, and that the first strategy dramatically improves results. As in the case of Gibbs sampling, these strategies are applicable to a much wider class of models. They are shown to provide more uniform importance sampling weights and lead to additional Rao‐Blackwellization of estimators.
A new method for estimating finite‐population quantiles using auxiliary information
Authors: Mak Tak K. , Kuk Anthony 
Published: June 2006

AbstractA computationally simple method for estimating finite‐population quantiles in the presence of auxiliary information is proposed. An algorithm is also found for implementing related approaches for estimating quantiles, including that of Rao et al. (1990), obtained from inverting difference‐type estimators of the distribution function. The proposed estimation procedure can be seen as a one‐step iteration of the suggested algorithm and is asymptotically equivalent to the limiting estimator. In particular, the proposed method yields a simple and efficient way of approximating Rao et al.'s estimator. Simulation studies based on two real populations show that the approximation can be very satisfactory even for small to moderate samples.