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作者：Pronzato, L
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur
摘要：We consider the situation where one has to maximize a function eta(theta, x) with respect to x is an element of R-q, when a is unknown and estimated by least squares through observations y(k) = f(inverted perpendicular)(x(k))theta + epsilon (k), with epsilon (k) some random error. Classical applications are regulation and extremum control problems. The approach we adopt corresponds to maximizing the sum of the current estimated objective and a penalization for poor estimation: x(k+1) maximizes...
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作者：Juditsky, A; Nemirovski, A
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Technion Israel Institute of Technology
摘要：We consider the problem of estimating an unknown function f from N noisy observations on a random grid. In this paper we address the following aggregation problem: given M functions f(1),...,f(M) find an aggregated estimator which approximates f nearly as well as the best convex combination f* of f(1),...,f(M). We propose algorithms which provide approximations of f* with expected L-2 accuracy O(N(-1/)4 ln(1/4) M). We show that this approximation rate cannot be significantly improved. We discu...
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作者：Morgan, JP; Bailey, RA
作者单位：Old Dominion University; University of London; Queen Mary University London
摘要：Designs for sets of experimental units with many blocking factors are studied. It is shown that if the set of blocking factors satisfies a certain simple condition then the information matrix for the design has a simple form. In consequence, a design is optimal if it is optimal with respect to one particular blocking factor and regular with respect to all the rest, in a sense which is made precise in the paper. This encompasses several previous results for optimal designs with more than one bl...
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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...
