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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：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：Loh, WL; Lam, TK
作者单位：National University of Singapore; Dell Incorporated; Dell EMC
摘要：This article considers the estimation of structured correlation matrices in infinitely differentiable Gaussian random field models. The problem is essentially motivated by the stochastic modeling of smooth deterministic responses in computer experiments. In particular, the log-likelihood function is determined explicitly in closed-form and the sieve maximum likelihood estimators are shown to be strongly consistent under mild conditions.
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作者：Hall, P; Rau, C
作者单位：Australian National University; Commonwealth Scientific & Industrial Research Organisation (CSIRO)
摘要：We suggest a sequential, or tracking, algorithm for estimating a smooth fault line in a response surface. The method starts with an approximation to a point on the line, and from there the line is tracked as it meanders through the plane. The technique differs from recent approaches in that it does not require a large part of the plane to be searched for evidence of a fault line. This offers potential computational savings, and produces a method that is invariant under rotations of coordinate ...
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作者：Wellner, JA; Zhang, Y
作者单位：University of Washington; University of Washington Seattle; State University System of Florida; University of Central Florida
摘要：We study two estimators of the mean function of a counting process based on panel count data. The setting for panel count data is one in which n independent subjects, each with a counting process with common mean function, are observed at several possibly different times during a study. Following a model proposed by Schick and Yu, we allow the number of observation times, and the observation times themselves, to be random variables. Our goal is to estimate the mean function of the counting pro...
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作者：Romano, JP; Wolf, M
作者单位：Stanford University; Universidad Carlos III de Madrid
摘要：Given a sample X-1,...,X-n from a distribution F, the problem of constructing nonparametric confidence intervals for the mean mu (F) is considered. Unlike bootstrap procedures or those based on normal approximations, we insist an any procedure being truly nonparametric in the sense that the probability that the confidence interval contains mu (F) based on a sample of size n from F be at least 1 - alpha for all F and all n. Bahadur and Savage proved it is impossible to find an effective (or bou...
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作者：Spokoiny, VG
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：We consider a nonparametric diffusion process whose drift and diffusion coefficients are nonparametric functions of the state variable. The goal is to estimate the unknown drift coefficient. We apply a locally linear smoother with a data-driven bandwidth choice. The procedure is fully adaptive and nearly optimal up to a log log factor. The results about the quality of estimation are nonasymptotic and do not require any ergodic or mixing properties of the observed process.
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作者：Kochar, SC; Mukerjee, H; Samaniego, FJ
作者单位：Indian Statistical Institute; Indian Statistical Institute Kolkata; University of California System; University of California Davis; Wichita State University
摘要：In survival analysis and in the analysis of life tables an important biometric function of interest is the life expectancy at age x, M(x), defined by M(x)= E[X - x\X > z], where X is a lifetime. EA is called the mean residual life function. In many applications it is reasonable to assume that M is decreasing (DMRL) or increasing (IMRL); we write decreasing (increasing) for nonincreasing (nondecreasing). There is some literature on empirical estimators of M and their properties. Although tests ...
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作者：Shapiro, A
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：We discuss in this paper asymptotics of locally optimal solutions of maximum likelihood and, more generally, M-estimation procedures in cases where the true value of the parameter vector lies on the boundary of the parameter set S. We give a counterexample showing that regularity of S in the sense of Clarke is not; sufficient for asymptotic equivalence of rootn-consistent locally optimal M-estimators. We argue further that stronger properties, such as so-called near convexity or prox-regularit...
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作者：Peskir, G; Shiryaev, AN
作者单位：Aarhus University; University of Zagreb; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences
摘要：We present the explicit solution of the Bayesian problem of sequential testing of two simple hypotheses about the intensity of an observed Poisson process. The method of proof consists of reducing the initial problem to a free-boundary differential-difference Stephan problem and solving the latter by use of the principles of smooth and continuous fit. A rigorous proof of the optimality of the Wald's sequential probability ratio test in the variational formulation of the problem is obtained as ...
