bluuebunny/crossref_metadata_2025_split huggingface dataset:
Tables for the Friedman rank test
Authors: Martin Louise , Leblanc Raymond , Toan Nguyen Ky 
Published: June 2006

AbstractThis note presents tables for Friedman's test for two‐way analysis of variance by ranks. These tables are more accurate than those that are presented in the literature. After intensive simulations, we have found for particular critical values some discrepancies with tables published earlier. The tables are also more extensive than those previously available.
Fisher information and maximum‐likelihood estimation of covariance parameters in Gaussian stochastic processes
Authors: Abt Markus , Welch William J. 
Published: June 2006

AbstractThe inverse of the Fisher information matrix is commonly used as an approximation for the covariance matrix of maximum‐likelihood estimators. We show via three examples that for the covariance parameters of Gaussian stochastic processes under infill asymptotics, the covariance matrix of the limiting distribution of their maximum‐likelihood estimators equals the limit of the inverse information matrix. This is either proven analytically or justified by simulation. Furthermore, the limiting behaviour of the trace of the inverse information matrix indicates equivalence or orthogonality of the underlying Gaussian measures. Even in the case of singularity, the estimator of the process variance is seen to be unbiased, and also its variability is approximated accurately from the information matrix.
The score function and a comparison of various adjustments of the profile likelihood
Authors: Davison A. C. , Stafford J. E. 
Published: June 2006

AbstractSeveral adjustments of the profile likelihood have the common effect of reducing the bias of the associated score function. Hence expansions for the adjusted score functions differ by a term,Dξ, that has small asymptotic order (n−½). The effect ofDξon other quantities of interest is studied. In particular, we find the bias and variance of the adjusted maximum‐likelihood estimate to be relatively unaffected, while differences in the Bartlett correction depend onDξin a simple way.
A bootstrap procedure in linear regression with nonstationary errors
Authors: Yeh Arthur B. 
Published: June 2006

AbstractIn the context of linear regression with dependent and nonstationary errors, the classical moving‐block bootstrap (MBB) fails to capture the nonstationarity of the errors. A new bootstrap procedure called the blocking external bootstrap (BEB) is proposed to overcome the problem. The consistency of the BEB in estimating the variance of the least‐squares estimator is studied in the case of α‐mixing and nonstationary sequence of errors. It is shown that the BEB only achieves partial correction if the block size is fixed. Complete consistency is achieved by the BEB when the block size is allowed to go to infinity. We also study the first‐order consistency of the least squares estimator based on the BEB. A simulation study is carried out to assess the performance of the BEB versus the MBB in estimating the variance of the least‐squares estimator. Finally, some open problems are discussed.
Propriétés statistiques des copules de valeurs extrêmes bidimensionnelles
Authors: Ghoudi Kilani , Khoudraji Abdelhaq , Rivest Et Louis‐Paul 
Published: June 2006

AbstractLet (X, Y) be a bivariate random vector whose distribution function H(x, y) belongs to the class of bivariate extreme‐value distributions. If F1 and F2 are the marginals of X and Y, then H(x, y) = C{F1(x),F2(y)}, where C is a bivariate extreme‐value dependence function. This paper gives the joint distribution of the random variables Z = {log F1(X)}/{log F1(X)F2(Y)} and W = C{F1{(X),F2(Y)}. Using this distribution, an algorithm to generate random variables having bivariate extreme‐value distribution is présentés. Furthermore, it is shown that for any bivariate extreme‐value dependence function C, the distribution of the random variable W = C{F1(X),F2(Y)} belongs to a monoparametric family of distributions. This property is used to derive goodness‐of‐fit statistics to determine whether a copula belongs to an extreme‐value family.
Estimation in the multipath change point problem for correlated data
Authors: Joseph Lawrence , Vandal Alain C. , Wolfson David B. 
Published: June 2006

AbstractIn many experiments, several measurements on the same variable are taken over time, a geographic region, or some other index set. It is often of interest to know if there has been a change over the index set in the parameters of the distribution of the variable. Frequently, the data consist of a sequence of correlated random variables, and there may also be several experimental units under observation, each providing a sequence of data. A problem in ascertaining the boundaries between the layers in geological sedimentary beds is used to introduce the model and then to illustrate the proposed methodology. It is assumed that, conditional on the change point, the data from each sequence arise from an autoregressive process that undergoes a change in one or more of its parameters. Unconditionally, the model then becomes a mixture of nonstationary autoregressive processes. Maximum‐likelihood methods are used, and results of simulations to evaluate the performance of these estimators under practical conditions are given.
Estimation of a multivariate mean with constraints on the norm
Authors: Marchand Eric 
Published: June 2006

AbstractEstimation of the mean θ of a spherical distribution with prior knowledge concerning the norm ||θ|| is considered. The best equivariant estimator is obtained for the local problem ||θ|| = λ0, and its risk is evaluated. This yields a sharp lower bound for the risk functions of a large class of estimators. The risk functions of the best equivariant estimator and the best linear estimator are compared under departures from the assumption ||θ|| = λ0.
Estimation of the mutagenic potency of environmental chemicals using short‐term bioassay
Authors: Gentleman Jane F. , Whitmore G. A. 
Published: June 2006

AbstractThe Ames Salmonella test is a widely used bioassay method for assessing the mutagenic potency of a potential carcinogen. The test is quick and reliable, and exploits the correlation that exists between mutagenic potential and carcinogenic potential. The data for this case study came from an international study involving 20 laboratories in nine countries. The laboratories participated in a designed experiment in which substances (complex chemical mixtures of the type encountered in the environment) were evaluated for mutagenicity using the Ames test. A stringent protocol was followed. The study's principal aim was to investigate intra‐ and inter‐laboratory variation in test results. The data consist of counts of revertant Salmonella colonies at each of six dose levels of a substance. The data were obtained for each of five test substances from each participating laboratory. The bioassays were carried out according to a prescribed factorial experimental design. Three sets of analysts participated in this case study. They were asked to model the dose‐response relationship for two substances, to develop an index of the strength of the relationship, and to assess intra‐ and inter‐laboratory variation in bioassay results.
An application of the Bernoulli part to local limit theorems for moving averages on stationary sequences
Authors: Dabrowski André Robert , Mcdonald David 
Published: June 2006

AbstractWe consider partial sums Sn of a general class of stationary sequences of integer‐valued random variables, and we provide sufficient conditions for Sn to satisfy a local limit theorem. To prove this result, we introduce a concept called the Bernoulli part. The amount of Bernoulli part in Sn determines the extent to which the density of Sn is relatively flat. If in addition Sn satisfies a global central limit theorem, the local limit theorem follows.
A simple test of symmetry about an unknown median
Authors: Cabilio Paul , Masaro Joe 
Published: June 2006

AbstractA simple test statistic for testing symmetry of a distribution function about an unknown value is presented. The asymptotic distributions under symmetry and asymmetry are derived. Using the normal as a “calibration” distribution, the critical values of the test are calculated by Monte Carlo methods. Comparisons with other tests indicate that this procedure performs well.
Robust estimation of variance components
Authors: Gervini Daniel , Yohai Victor J. 
Published: June 2006

AbstractNew robust estimates for variance components are introduced. Two simple models are considered: the balanced one‐way classification model with a random factor and the balanced mixed model with one random factor and one fixed factor. However, the method of estimation proposed can be extended to more complex models. The new method of estimation we propose is based on the relationship between the variance components and the coefficients of the least‐mean‐squared‐error predictor between two observations of the same group. This relationship enables us to transform the problem of estimating the variance components into the problem of estimating the coefficients of a simple linear regression model. The variance‐component estimators derived from the least‐squares regression estimates are shown to coincide with the maximum‐likelihood estimates. Robust estimates of the variance components can be obtained by replacing the least‐squares estimates by robust regression estimates. In particular, a Monte Carlo study shows that for outlier‐contaminated normal samples, the estimates of variance components derived from GM regression estimates and the derived test outperform other robust procedures.
Laplace approximations for censored linear regression models
Authors: Papandonatos George D. , Geisser Seymour 
Published: June 2006

AbstractWe consider approximate Bayesian inference about scalar parameters of linear regression models with possible censoring. A second‐order expansion of their Laplace posterior is seen to have a simple and intuitive form for logconcave error densities with nondecreasing hazard functions. The accuracy of the approximations is assessed for normal and Gumbel errors when the number of regressors increases with sample size. Perturbations of the prior and the likelihood are seen to be easily accommodated within our framework. Links with the work of DiCiccioet al.(1990) and Viveros and Sprott (1987) extend the applicability of our results to conditional frequentist inference based on likelihood‐ratio statistics.
Pearson‐type goodness‐of‐fit tests for regression
Authors: Akritas M. G. , Torbeyns A. F. 
Published: June 2006

AbstractA procedure for testing the goodness of fit of linear regression models is introduced. For a given partition of the real line into cells, the proposed test is a quadratic form based on the vector of observed minus expected frequencies of the residuals obtained by maximum‐likelihood estimation of the regression parameters. The quadratic form is of the same computational difficulty as the traditional Pearson‐type tests with uncensored data. A statistic based on only one cell is particularly easy to apply and is used for testing the normality assumption in a real data set from astronomy. A simulation study examines the finite‐sample properties of the proposed tests.
On testing the number of components in finite mixture models with known relevant component distributions
Authors: Chen Jiahua , Cheng Ping 
Published: June 2006

AbstractThe limiting distribution of the log‐likelihood‐ratio statistic for testing the number of components in finite mixture models can be very complex. We propose two alternative methods. One method is generalized from a locally most powerful test. The test statistic is asymptotically normal, but its asymptotic variance depends on the true null distribution. Another method is to use a bootstrap log‐likelihood‐ratio statistic which has a uniform limiting distribution in [0,1]. When tested against local alternatives, both methods have the same power asymptotically. Simulation results indicate that the asymptotic results become applicable when the sample size reaches 200 for the bootstrap log‐likelihood‐ratio test, but the generalized locally most powerful test needs larger sample sizes. In addition, the asymptotic variance of the locally most powerful test statistic must be estimated from the data. The bootstrap method avoids this problem, but needs more computational effort. The user may choose the bootstrap method and let the computer do the extra work, or choose the locally most powerful test and spend quite some time to derive the asymptotic variance for the given model.
Bayesian analysis of screening data: Application to AIDS in blood donors
Authors: Gastwirth Joseph L. , Johnson Wesley O. , Reneau Dana M. 
Published: June 2006

AbstractThe rapid increase in the number of AIDS cases during the 1980s and the spread of the disease from the high‐risk groups into the general population has created widespread concern. In particular, assessing the accuracy of the screening tests used to detect antibodies to the HIV (AIDS) virus in donated blood and determining the prevalance of the disease in the population are fundamental statistical problems.Because the prevalence of AIDS varies widely by geographic region and data on the number of infected blood donors are published regularly, Bayesian methods, which utilize prior results and update them as new data become available, are quite useful. In this paper we develop a Bayesian procedure for estimating the prevalence of a rare disease, the sensitivity and specificity of the screening tests, and the predictive value of a positive or negative screening test. We apply the procedure to data on blood donors in the United States and in Canada. Our results augment those described in Gastwirth (1987) using classical methods. Indeed, we show that the inclusion of sound prior knowledge into the statistical analysis does not yield sufficiently precise estimates of the predictive value of a positive test. Hence confirmatory testing is needed to obtain reliable estimates.The emphasis of the Bayesian predictive paradigm on prediction intervals for future data yields a valuable insight. We demonstrate that using them might have detected a decline in the specificity of the most frequently used screening test earlier than it apparently was.
Multivariate extreme‐value distributions with applications to environmental data
Authors: Joe Harry 
Published: June 2006

AbstractSome parametric families of multivariate extreme‐value distributions have been proposed in recent years; several additional parametric families are derived here. The parametric models are fitted, using numerical maximum likelihood, to some environmental multivariate extreme data sets consisting of extreme concentrations of a pollutant at several monitoring stations in a region. Some multivariate nonnormal data analysis techniques are proposed to aid in the likelihood analysis. The new models, together with previous models, appear to be adequate for inferences in that they cover a wide range of possible dependence patterns.
Variation in height acceleration in the Fels growth data
Authors: Ramsay J.O. , Altman N. , BOCK R. Darrell 
Published: June 2006

AbstractThe Fels growth data record at half‐yearly intervals the heights of children from birth to adulthood, and are the basis for pediatricians' growth charts used throughout North America. Aspects of human growth are the subject of a large medical and statistical literature. This paper uses smoothing splines to study the variation in height acceleration. By use of a functional version of principal‐components analysis, we find that variation in the acceleration curve is essentially three‐dimensional in nature. Evidence for a small growth spurt between the ages of six and eight, reported for data collected in Switzerland, is examined, and little support is found for the existence of this phenomenon in the Fels data.
Conditions for consistent estimation in mixed‐effects models for binary matched‐pairs data
Authors: Neuhaus J.M. , Kalbfleisch J.D. , Hauck W.W. 
Published: June 2006

AbstractParametric mixed‐effects logistic models can provide effective analysis of binary matched‐pairs data. Responses are assumed to follow a logistic model within pairs, with an intercept which varies across pairs according to a specified family of probability distributions G. In this paper we give necessary and sufficient conditions for consistent covariate effect estimation and present a geometric view of estimation which shows that when the assumed family of mixture distributions is rich enough, estimates of the effect of the binary covariate are typically consistent. The geometric view also shows that under the conditions for consistent estimation, the mixed‐model estimator is identical to the familar conditional‐likelihood estimator for matched pairs. We illustrate the findings with some examples.
Approximate and estimated saddlepoint approximations
Authors: Ohman‐Strickland Pamela , Casella George 
Published: June 2006

AbstractClassical saddlepoint methods, which assume that the cumulant generating function is known, result in an approximation to the distribution that achieves an error of orderO(n−1). The authors give a general theorem to address the accuracy of saddlepoint approximations in which the cumulant generating function has been estimated or approximated. In practice, the resulting saddlepoint approximations are typically of the orderO(n−1/2). The authors give simulation results for small sample examples to compare estimated saddlepoint approximations.
Box‐Cox transformations in linear models: Large sample theory and tests of normality
Authors: Chen Gemai , Lockhart Richard A. , Stephens Michael A. 
Published: June 2006

AbstractThe authors provide a rigorous large sample theory for linear models whose response variable has been subjected to the Box‐Cox transformation. They provide a continuous asymptotic approximation to the distribution of estimators of natural parameters of the model. They show, in particular, that the maximum likelihood estimator of the ratio of slope to residual standard deviation is consistent and relatively stable. The authors further show the importance for inference of normality of the errors and give tests for normality based on the estimated residuals. For non‐normal errors, they give adjustments to the log‐likelihood and to asymptotic standard errors.
Exact and approximate sum representations for the Dirichlet process
Authors: Ishwaran Hemant , Zarepour Mahmoud 
Published: June 2006

AbstractThe Dirichlet process can be regarded as a random probability measure for which the authors examine various sum representations. They consider in particular the gamma process construction of Ferguson (1973) and the “stick‐breaking” construction of Sethuraman (1994). They propose a Dirichlet finite sum representation that strongly approximates the Dirichlet process. They assess the accuracy of this approximation and characterize the posterior that this new prior leads to in the context of Bayesian nonpara‐metric hierarchical models.
Linear functional regression: The case of fixed design and functional response
Authors: Cuevas Antonio , Febrero Manuel , Fraiman Ricardo 
Published: June 2006

AbstractThe authors consider the problem of simple linear regression when the exogenous and endogenous variables are functional and the design is fixed. They propose an estimator for the underlying linear operator and prove its consistency under some conditions which ensure that the design is sufficiently informative. They consider the classical calibration (or inverse regression) problem and analyze a consistent estimator. They also give a simulation study. The proposed method is not hard to implement in practice.
Smooth estimates of normal mixtures
Authors: Tong Barbara , Viele Kert 
Published: June 2006

AbstractPosterior distributions for mixture models often have multiple modes, particularly near the boundaries of the parameter space where the component variances are small. This multimodality results in predictive densities that are extremely rough. The authors propose an adjustment of the standard normal‐inverse‐gamma prior structure that directly controls the ratio of the largest component variance to the smallest component variance. The prior adjustment smooths out modes near the boundary of the parameter space, producing more reasonable estimates of the predictive density.
Adaptive estimation in partially linear autoregressive models
Authors: Gao Jiti , Yee Thomas 
Published: June 2006

AbstractThe authors consider a partially linear autoregressive model and construct kernel‐based estimates for both the parametric and nonparametric components. They propose an estimation procedure for the model and illustrate it through simulated and real data. Their work shows that the proposed estimation procedure not only has good asymptotic properties but also works well numerically. It also suggests that a partially linear autoregression is more appropriate than a completely nonparametric autoregression for some sets of data.
Differential equation models for statistical functions
Authors: Ramsay James O. 
Published: June 2006

AbstractDifferential equations have been used in statistics to define functions such as probability densities. But the idea of using differential equation formulations of stochastic models has a much wider scope. The author gives several examples, including simultaneous estimation of a regression model and residual density, monotone smoothing, specification of a link function, differential equation models of data, and smoothing over complicated multidimensional domains. This paper aims to stimulate interest in this approach to functional estimation problems, rather than provide carefully worked out methods.
Effects of omitting a covariate in poisson models when the data are balanced
Authors: Petersen Martin R. , Deddens James A. 
Published: June 2006

AbstractThe authors show that for balanced data, the estimates of effects of interest and of their standard errors are unaffected when a covariate is removed from a multiplicative Poisson model. As they point out, this is not verified in the analogous linear model, nor in the logistic model. In the first case, only the estimated coefficients remain the same, while in the second case, both the estimated effects and their standard errors can change.
Spatial prediction and temporal backcasting for environmental fields having monotone data patterns
Authors: Le Nhu , Sun Li , Zidek James V. 
Published: June 2006

AbstractThe authors develop a methodology for predicting unobserved values in a conditionally lognormal random spatial field like those commonly encountered in environmental risk analysis. These unobserved values are of two types. The first come from spatial locations where the field has never been monitored, the second, from currently monitored sites which have been only recently installed. Thus the monitoring data exhibit a monotone pattern, resembling a staircase whose highest step comes from the oldest monitoring sites. The authors propose a hierarchical Bayesian approach using the lognormal sampling distribution, in conjunction with a conjugate generalized Wishart distribution. This prior distribution allows different degrees of freedom to be fitted for individual steps, taking into account the differential amounts of information available from sites at the different steps in the staircase. The resulting hierarchical model is a predictive distribution for the unobserved values of the field. The method is demonstrated by application to the ambient ozone field for the southwestern region of British Columbia.