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作者：Ghosal, S; Sen, A; van der Vaart, W
作者单位：Vrije Universiteit Amsterdam; University of Hyderabad
摘要：We consider the problem of testing monotonicity of the regression function in a nonparametric regression model. We introduce test statistics that are functionals of a certain natural U-process. We study the limiting distribution of these test statistics through strong approximation methods and the extreme value theory for Gaussian processes. We show that the tests are consistent against general alternatives.
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作者：Martinussen, T; Scheike, TH
作者单位：University of Copenhagen; University of Copenhagen
摘要：In this work we study additive dynamic regression models for longitudinal data. These models provide a flexible and nonparametric method for investigating the time-dynamics of longitudinal data. The methodology is aimed at data where measurements are recorded at random time points. We model the conditional mean of responses given the full internal history and possibly time-varying covariates. We derive the asymptotic distribution for a new nonparametric least squares estimator of the cumulativ...
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作者：Genovese, CR; Wasserman, L
作者单位：Carnegie Mellon University
摘要：Gaussian mixtures provide a convenient method of density estimation that lies somewhere between parametric models and kernel density estimators. When the number of components of the mixture is allowed to increase as sample size increases, the model is called a mixture sieve. We establish a bound on the rate of convergence in Hellinger distance for density estimation using the Gaussian mixture sieve assuming that the true density is itself a mixture of Gaussians; the underlying mixing measure o...
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作者：Bartolucci, F; Forcina, A
作者单位：University of Perugia
摘要：Multivariate Totally Positive (MTP2) binary distributions have been studied in many fields, such as statistical mechanics, computer storage and latent variable models. We show that MTP2 is equivalent to the requirement that the parameters of a saturated log-linear model belong to a convex cone, and we provide a Fisher-scoring algorithm for maximum likelihood estimation. We also show that the asymptotic distribution of the log-likelihood ratio is a mixture of chi-squares (a distribution known a...
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作者：Meyer, M; Woodroofe, M
作者单位：University System of Georgia; University of Georgia; University of Michigan System; University of Michigan
摘要：For the problem of estimating a regression function, mu say, subject to shape constraints, like monotonicity or convexity it is argued that the divergence of the maximum likelihood estimator provides a useful measure of the effective dimension of the model. Inequalities are derived for the expected mean squared error of the maximum likelihood estimator and the expected residual sum of squares. These generalize equalities from the case of linear regression. As an application, it is shown that t...
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作者：Huang, JHZ; Kooperberg, C; Stone, CJ; Truong, YK
作者单位：University of Pennsylvania; Fred Hutchinson Cancer Center; University of California System; University of California Berkeley; University of North Carolina; University of North Carolina Chapel Hill; National University of Singapore
摘要：The logarithm of the relative risk function in a proportional hazards model involving one or more possibly time-dependent covariates is treated as a specified sum of a constant term, main effects, and selected interaction terms. Maximum partial likelihood estimation is used, where the maximization is taken over a suitably chosen finite-dimensional estimation space, whose dimension increases with the sample size and which is constructed from linear spaces of functions of one covariate and their...
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作者：Settimi, R; Smith, JQ
作者单位：University of Chicago; University of Warwick
摘要：We study the geometry of the parameter space for Bayesian directed graphical models with hidden variables that have a tree structure and where all the nodes are binary. We show that the conditional independence statements implicit in such models can be expressed in terms of polynomial relationships among the central moments. This algebraic structure will enable us to identify the inequality constraints on the space of the manifest variables that are induced by the conditional independence assu...
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作者：Breidt, FJ; Opsomer, JD
作者单位：Colorado State University System; Colorado State University Fort Collins; Iowa State University; Iowa State University
摘要：Estimation of finite population totals in the presence of auxiliary information is considered. A class of estimators based on local polynomial regression is proposed. Like generalized regression estimators, these estimators are weighted linear combinations of study variables, in which the weights are calibrated to known control totals, but the assumptions on the superpopulation model are considerably weaker. The estimators are shown to be asymptotically design-unbiased and consistent under mil...
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作者：Madsen, J
作者单位：University of Copenhagen
摘要：An extension of the class of GS-LCI normal models introduced by Andersson and Madsen is defined and studied. The models are defined in terms of symmetry restrictions given by a finite group and conditional independence restrictions given by an acyclic directed graph. Maximum likelihood estimation of the parameters in the models is discussed.
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作者：Frigessi, A; Gåsemyr, J; Rue, H
作者单位：University of Oslo; Norwegian University of Science & Technology (NTNU)
摘要：Two coupled Gibbs sampler chains, both with invariant probability density pi, are run in parallel so that the chains are negatively correlated. We define an asymptotically unbiased estimator of the pi -expectation E( f(X)) which achieves significant variance reduction with respect to the usual Gibbs sampler at comparable computational cost. The variance of the estimator based on the new algorithm is always smaller than the variance of a single Gibbs sampler chain, if pi is attractive and f is ...
