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作者：Tang, Runlong; Banerjee, Moulinath; Michailidis, George
作者单位：University of Michigan System; University of Michigan
摘要：We consider a two-stage procedure (TSP) for estimating an inverse regression function at a given point, where isotonic regression is used at stage one to obtain an initial estimate and a local linear approximation in the vicinity of this estimate is used at stage two. We establish that the convergence rate of the second-stage estimate can attain the parametric n(1/2) rate. Furthermore, a bootstrapped variant of TSP (BTSP) is introduced and its consistency properties studied. This variant manag...
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作者：Fan, Jianqing; Liao, Yuan; Mincheva, Martina
作者单位：Princeton University
摘要：The variance-covariance matrix plays a central role in the inferential theories of high-dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By assuming sparse error cova...
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作者：Arias-Castro, Ery; Candes, Emmanuel J.; Plan, Yaniv
作者单位：University of California System; University of California San Diego; Stanford University; California Institute of Technology
摘要：Testing for the significance of a subset of regression coefficients in a linear model, a staple of statistical analysis, goes back at least to the work of Fisher who introduced the analysis of variance (ANOVA). We study this problem under the assumption that the coefficient vector is sparse, a common situation in modern high-dimensional settings. Suppose we have p covariates and that under the alternative, the response only depends upon the order of p(1-alpha) of those, 0 <= alpha <= 1. Under ...
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作者：Negahban, Sahand; Wainwright, Martin J.
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：We study an instance of high-dimensional inference in which the goal is to estimate a matrix circle minus* is an element of R-m1xm2 on the basis of N noisy observations. The unknown matrix circle minus* is assumed to be either exactly low rank, or near low-rank, meaning that it can be well-approximated by a matrix with low rank. We consider a standard M-estimator based on regularization by the nuclear or trace norm over matrices, and analyze its performance under high-dimensional scaling. We d...
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作者：Lerasle, Matthieu
作者单位：Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National des Sciences Appliquees de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We propose a block-resampling penalization method for marginal density estimation with nonnecessary independent observations. When the data are beta or tau-mixing, the selected estimator satisfies oracle inequalities with leading constant asymptotically equal to 1. We also prove in this setting the slope heuristic, which is a data-driven method to optimize the leading constant in the penalty.
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作者：Ait-Sahalia, Yacine; Jacod, Jean
作者单位：Princeton University; National Bureau of Economic Research; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite
摘要：We propose statistical tests to discriminate between the finite and infinite activity of jumps in a semimartingale discretely observed at high frequency. The two statistics allow for a symmetric treatment of the problem: we can either take the null hypothesis to be finite activity, or infinite activity. When implemented on high-frequency stock returns, both tests point toward the presence of infinite-activity jumps in the data.
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作者：Seijo, Emilio; Sen, Bodhisattva
作者单位：Columbia University
摘要：This paper deals with the consistency of the nonparametric least squares estimator of a convex regression function when the predictor is multidimensional. We characterize and discuss the computation of such an estimator via the solution of certain quadratic and linear programs. Mild sufficient conditions for the consistency of this estimator and its subdifferentials in fixed and stochastic design regression settings are provided.
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作者：Cai, T. Tony; Low, Mark G.
作者单位：University of Pennsylvania
摘要：A general lower bound is developed for the minimax risk when estimating an arbitrary functional. The bound is based on testing two composite hypotheses and is shown to be effective in estimating the nonsmooth functional 1/n Sigma vertical bar theta(i)vertical bar from an observation Y similar to N (theta, I-n). This problem exhibits some features that are significantly different from those that occur in estimating conventional smooth functionals. This is a setting where standard techniques fai...
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作者：Qian, Min; Murphy, Susan A.
作者单位：University of Michigan System; University of Michigan
摘要：Because many illnesses show heterogeneous response to treatment, there is increasing interest in individualizing treatment to patients [Arch. Gen. Psychiatry 66 (2009) 128-133]. An individualized treatment rule is a decision rule that recommends treatment according to patient characteristics. We consider the use of clinical trial data in the construction of an individualized treatment rule leading to highest mean response. This is a difficult computational problem because the objective functio...
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作者：Khare, Kshitij; Rajaratnam, Bala
作者单位：State University System of Florida; University of Florida; Stanford University
摘要：Gaussian covariance graph models encode marginal independence among the components of a multivariate random vector by means of a graph G. These models are distinctly different from the traditional concentration graph models (often also referred to as Gaussian graphical models or covariance selection models) since the zeros in the parameter are now reflected in the covariance matrix E, as compared to the concentration matrix Omega = Sigma(-1) The parameter space of interest for covariance graph...
