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作者：Ghosal, S
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：Mixture models for density estimation provide a very useful set up for the Bayesian or the maximum likelihood approach. For a density on the unit interval, mixtures of beta densities form a flexible model. The class of Bernstein densities is a much smaller subclass of the beta mixtures defined by Bernstein polynomials, which can approximate any continuous density. A Bernstein polynomial prior is obtained by putting a prior distribution on the class of Bernstein densities. The posterior distrib...
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作者：Di Bucchianico, A; Einmahl, JHJ; Mushkudiani, NA
作者单位：Eindhoven University of Technology; Eindhoven University of Technology; Tilburg University
摘要：We present a new, natural way to construct nonparametric multivariate tolerance regions. Unlike the classical nonparametric tolerance intervals, where the endpoints are determined by beforehand chosen order statistics, we take the shortest interval, that contains a certain number of observations. We extend this idea to higher dimensions by replacing the class of intervals by a general class of indexing sets, which specializes to the classes of ellipsoids, hyperrectangles or convex sets. The as...
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作者：Einmahl, JHJ; De Haan, L; Piterbarg, VI
作者单位：Tilburg University; Erasmus University Rotterdam - Excl Erasmus MC; Erasmus University Rotterdam; Lomonosov Moscow State University
摘要：Let (X-1, Y-1),..., (X-n, Y-n) be a random sample from a bivariate distribution function F in the domain of max-attraction of a distribution function G. This G is characterised by the two extreme value indices and its spectral or angular measure. The extreme value indices determine both the marginals and the spectral measure determines the dependence structure of G. One of the main issues in multivariate extreme value theory is the estimation of this spectral measure. We construct a truly nonp...
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作者：Holst, M; Irle, A
作者单位：University of Kiel
摘要：The asymptotic classification risk for nearest neighbor procedures is well understood in the case of i.i.d. training sequences. In this article, we generalize these results to a class of dependent models including hidden Markov models. In the case where the observed patterns have Lebesgue densities, the asymptotic risk takes the same expression as in the i.i.d. case. For discrete distributions, we show that the asymptotic risk depends on the rule used for breaking ties of equal distances.
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作者：Friedman, JH
作者单位：Stanford University
摘要：Function estimation/approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest-descent minimization. A general gradient descent boosting paradigm is developed for additive expansions based on any fitting criterion. Specific algorithms are presented for least-squares, least absolute deviation, and Huber-M loss functions for regression, and multiclass logistic likel...
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作者：Delgado, MA; Manteiga, WG
作者单位：Universidad Carlos III de Madrid; Universidade de Santiago de Compostela
摘要：This paper proposes a test for selecting explanatory variables in nonparametric regression. The test does not need to estimate the conditional expectation function given all the variables, but only those which are significant under the null hypothesis. This feature is computationally convenient and solves, in part, the problem of the curse of dimensionality when selecting regressors in a nonparametric context. The proposed test statistic is based on functionals of a U-process. Contiguous alter...
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作者：Galtchouk, L; Konev, V
作者单位：Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Tomsk State University
摘要：We consider the problem of parameter estimation for multidimensional continuous-time linear stochastic regression models with an arbitrary finite number of unknown parameters and with martingale noise. The main result of the paper claims that the unknown parameters can be estimated with prescribed mean-square precision in this general model providing a unified description of both discrete and continuous time process. Among the conditions on the regressors there is one bounding the growth of th...
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作者：Scheike, TH
作者单位：University of Copenhagen
摘要：We present a non-parametric survival model with two time-scales. The time-scales are equivalent up to a constant that varies over the subjects. Covariate effects are modelled linearly on each time scale by additive Aalen models. Estimators of the cumulative intensities on the two time-scales are suggested by solving approximate local maximum likelihood estimating equations. The local estimating equations necessitate only the choice of one bandwidth. The estimators are provided with large sampl...
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作者：Ghosal, S; Van der Vaart, AW
作者单位：University of Minnesota System; University of Minnesota Twin Cities; Vrije Universiteit Amsterdam
摘要：We study the rates of convergence of the maximum likelihood estimator (MLE) and posterior distribution in density estimation problems, where the densities are location or location-scale mixtures of normal distributions with the scale parameter lying between two positive numbers. The true density is also assumed to lie in this class with the true mixing distribution either compactly supported or having sub-Gaussian tails. We obtain bounds for Hellinger bracketing entropies for this class, and f...
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作者：Walther, G
作者单位：Stanford University
摘要：A special semiparametric model for a univariate density is introduced that allows analyzing a number of problems via appropriate transformations. Two problems treated in some detail are testing for the presence of a mixture and detecting a wear-out trend in a failure rate. The analysis of the semiparametric model leads to an approach that advances the maximum likelihood theory of the Grenander estimator to a multiscale analysis. The construction of the corresponding test statistic rests on an ...
