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作者：Loh, Wei-Liem
作者单位：National University of Singapore
摘要：This article introduces a method for estimating the smoothness of a stationary, isotropic Gaussian random field from irregularly spaced data. This involves novel constructions of higher-order quadratic variations and the establishment of the corresponding fixed-domain asymptotic theory. In particular, we consider: (i) higher-order quadratic variations using nonequispaced line transect data, (ii) second-order quadratic variations from a sample of Gaussian random field observations taken along a...
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作者：Giraud, Christophe; Roueff, Francois; Sanchez-Perez, Andres
作者单位：Universite Paris Saclay; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Centre National de la Recherche Scientifique (CNRS)
摘要：In this work, we study the problem of aggregating a finite number of predictors for nonstationary sub-linear processes. We provide oracle inequalities relying essentially on three ingredients: (1) a uniform bound of the 1 norm of the time varying sub-linear coefficients, (2) a Lipschitz assumption on the predictors and (3) moment conditions on the noise appearing in the linear representation. Two kinds of aggregations are considered giving rise to different moment conditions on the noise and m...
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作者：Bao, Zhigang; Lin, Liang-Ching; Pan, Guangming; Zhou, Wang
作者单位：Nanyang Technological University; National Cheng Kung University; National University of Singapore
摘要：Let Q = (Qi,...,Qn) be a random vector drawn from the uniform distribution on the set of all n! permutations of {1,2,...,n}. Let Z = (Z1,...,Zn), where Z(j) is the mean zero variance one random variable obtained by centralizing and normalizing Q(j), j = 1,...,n. Assume that X-i, i = 1,...,p are i.i.d. copies of 1 root p Z and X = Xp,n is the p x n random matrix with X-i as its ith row. Then S-n = XX* is called the p x n Spearman's rank correlation matrix which can be regarded as a high dimensi...
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作者：Brownlees, Christian; Joly, Emilien; Lugosi, Gabor
作者单位：Pompeu Fabra University; ICREA; Pompeu Fabra University; Pompeu Fabra University
摘要：The purpose of this paper is to discuss empirical risk minimization when the losses are not necessarily bounded and may have a distribution with heavy tails. In such situations, usual empirical averages may fail to provide reliable estimates and empirical risk minimization may provide large excess risk. However, some robust mean estimators proposed in the literature may be used to replace empirical means. In this paper, we investigate empirical risk minimization based on a robust estimate prop...
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作者：Spokoiny, Vladimir; Zhilova, Mayya
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Humboldt University of Berlin; Moscow Institute of Physics & Technology; Russian Academy of Sciences; HSE University (National Research University Higher School of Economics)
摘要：A multiplier bootstrap procedure for construction of likelihood-based confidence sets is considered for finite samples and a possible model misspecification. Theoretical results justify the bootstrap validity for a small or moderate sample size and allow to control the impact of the parameter dimension p: the bootstrap approximation works if p(3)/n is small. The main result about bootstrap validity continues to apply even if the underlying parametric model is misspecified under the so-called s...
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作者：Bhattacharyya, Sharmodeep; Bickel, Peter J.
作者单位：University of California System; University of California Berkeley; Oregon State University
摘要：Analysis of stochastic models of networks is quite important in light of the huge influx of network data in social, information and bio sciences, but a proper statistical analysis of features of different stochastic models of networks is still underway. We propose bootstrap subsampling methods for finding empirical distribution of count features or moments (Bickel, Chen and Levina [Ann. Statist. 39 (2011) 2280-2301]) and smooth functions of these features for the networks. Using these methods,...
