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作者：Albers, W; Boon, PC; Kallenberg, WCM
作者单位：University of Twente
摘要：A pretest procedure consists of a preliminary test on a nuisance parameter, investigating whether it equals a given value or not, followed by the main testing problem on the parameter of interest. In case of acceptance of the preliminary test, the main test is applied in the restricted family with the given value of the nuisance parameter, while otherwise the test is performed in the complete family, including the nuisance parameter. For an appropriate class of tests, containing all standard f...
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作者：Hall, P; Heckman, NE
作者单位：Australian National University; University of British Columbia
摘要：A new approach to testing. for monotonicity of a regression mean, not requiring computation of a curve estimator or a bandwidth, is suggested. It is based on the notion of running gradients over short, intervals, although from some viewpoints it may be regarded as an analogue for monotonicity testing of the dip/excess mass approach for testing modality hypotheses about densities. Like the latter methods, the new technique does not suffer difficulties caused by almost-Bat parts of the target fu...
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作者：Goldenshluger, A; Greenshtein, E
作者单位：University of Haifa; Technion Israel Institute of Technology
摘要：This paper addresses the topic of model selection in regression. We emphasize the case of two models, testing which model provides a better prediction based on n observations. Within a family of selection rules, based on maximizing a penalized log-likelihood under a normal model, we search for asymptotically minimax rules over a class G of possible joint distributions of the explanatory and response variables. For the class g of multivariate normal joint distributions it is shown that asymptot...
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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：Laurent, B; Massart, P
作者单位：Universite Paris Saclay
摘要：We consider the problem of estimating parallel tos parallel to (2) when s belongs to some separable Hilbert space and one observes the Gaussian process Y(t) = [s, t] + sigmaL(t), for all t is an element of H, where L is some Gaussian isonormal process. This framework allows us in particular to consider the classical Gaussian sequence model for which H = l(2)(N*) and L(t) = Sigma (lambda greater than or equal to1)t(lambda)epsilon (lambda), where (epsilon (lambda))(lambda greater than or equal t...
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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：Zuo, YJ; Serfling, R
作者单位：Arizona State University; Arizona State University-Tempe; University of Texas System; University of Texas Dallas
摘要：Statistical depth functions have become increasingly used in nonparametric inference for multivariate data. Here the contours of such functions are studied. Structural properties of the regions enclosed by contours, such as affine equivariance, nestedness, connectedness and compactness, and almost sure convergence results for sample depth contours, are established. Also, specialized results are established for some popular depth functions, including halfspace depth, and for the case of ellipti...
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作者：Lin, Y
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：To deal with the curse of dimensionality in high-dimensional nonparametric problems, we consider using tensor product space ANOVA models, which extend the popular additive models and are able to capture interactions of any order. The multivariate function is given an ANOVA decomposition, that is, it is expressed as a constant plus the sum of functions of one variable (main effects), plus the sum of functions of two variables (two-factor interactions) and so on. We assume the interactions to be...
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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...
