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作者：Lugosi, Gabor; Mendelson, Shahar
作者单位：ICREA; Pompeu Fabra University; Barcelona School of Economics; Technion Israel Institute of Technology; Australian National University
摘要：We study the problem of estimating the mean of a random vector X given a sample of N independent, identically distributed points. We introduce a new estimator that achieves a purely sub-Gaussian performance under the only condition that the second moment of X exists. The estimator is based on a novel concept of a multivariate median.
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作者：Neykov, Matey; Lu, Junwei; Liu, Han
作者单位：Carnegie Mellon University; Princeton University; Northwestern University; Northwestern University
摘要：We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global structure of the underlying graph. Examples include testing the graph connectivity, the presence of a cycle of certain size, or the maximum degree of the graph. To begin with, we study the information-theoretic limits of a large family of combinatorial inferen...
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作者：Athey, Susan; Tibshirani, Julie; Wager, Stefan
作者单位：Stanford University
摘要：We propose generalized random forests, a method for nonparametric statistical estimation based on random forests (Breiman [Mach. Learn. 45 (2001) 5-32]) that can be used to fit any quantity of interest identified as the solution to a set of local moment equations. Following the literature on local maximum likelihood estimation, our method considers a weighted set of nearby training examples; however, instead of using classical kernel weighting functions that are prone to a strong curse of dime...
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作者：Wu, Yihong; Yang, Pengkun
作者单位：Yale University; University of Illinois System; University of Illinois Urbana-Champaign
摘要：We consider the problem of estimating the support size of a discrete distribution whose minimum nonzero mass is at least 1/k. Under the independent sampling model, we show that the sample complexity, that is, the minimal sample size to achieve an additive error of epsilon k with probability at least 0.1 is within universal constant factors of k/log k log(2) 1/epsilon, which improves the state-of-the-art result of k/epsilon(2) log k in [In Advances in Neural Information Processing Systems (2013...
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作者：Wei, Yuting; Wainwright, Martin J.; Guntuboyina, Adityanand
作者单位：University of California System; University of California Berkeley
摘要：We consider a compound testing problem within the Gaussian sequence model in which the null and alternative are specified by a pair of closed, convex cones. Such cone testing problem arises in various applications, including detection of treatment effects, trend detection in econometrics, signal detection in radar processing and shape-constrained inference in nonparametric statistics. We provide a sharp characterization of the GLRT testing radius up to a universal multiplicative constant in te...
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作者：Hsu, Hsiang-Ling; Ing, Ching-Kang; Tong, Howell
作者单位：National University Kaohsiung; National Tsing Hua University; University of Electronic Science & Technology of China; University of London; London School Economics & Political Science
摘要：Consider finite parametric time series models. I have n observations and k models, which model should I choose on the basis of the data alone is a frequently asked question in many practical situations. This poses the key problem of selecting a model from a collection of candidate models, none of which is necessarily the true data generating process (DGP). Although existing literature on model selection is vast, there is a serious lacuna in that the above problem does not seem to have received...
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作者：Qin, Likuan; Todorov, Viktor
作者单位：Northwestern University; Northwestern University
摘要：This paper develops a nonparametric estimator for the Levy density of an asset price, following an Ito semimartingale, implied by short-maturity options. The asymptotic setup is one in which the time to maturity of the available options decreases, the mesh of the available strike grid shrinks and the strike range expands. The estimation is based on aggregating the observed option data into nonparametric estimates of the conditional characteristic function of the return distribution, the deriva...
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作者：Hung, Kenneth; Fithian, William
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：Many statistical experiments involve comparing multiple population groups. For example, a public opinion poll may ask which of several political candidates commands the most support; a social scientific survey may report the most common of several responses to a question; or, a clinical trial may compare binary patient outcomes under several treatment conditions to determine the most effective treatment. Having observed the winner (largest observed response) in a noisy experiment, it is natura...
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作者：Bevilacqua, Moreno; Faouzi, Tarik; Furrer, Reinhard; Porcu, Emilio
作者单位：Universidad de Valparaiso; Universidad del Bio-Bio; University of Zurich; University of Zurich; Newcastle University - UK; Universidad de Atacama
摘要：We study estimation and prediction of Gaussian random fields with covariance models belonging to the generalized Wendland (GW) class, under fixed domain asymptotics. As for the Matern case, this class allows for a continuous parameterization of smoothness of the underlying Gaussian random field, being additionally compactly supported. The paper is divided into three parts: first, we characterize the equivalence of two Gaussian measures with GW covariance function, and we provide sufficient con...
