-
作者：Paindaveine, Davy; Verdebout, Thomas
作者单位：Universite Libre de Bruxelles; Universite Libre de Bruxelles
摘要：We revisit, in an original and challenging perspective, the problem of testing the null hypothesis that the mode of a directional signal is equal to a given value. Motivated by a real data example where the signal is weak, we consider this problem under asymptotic scenarios for which the signal strength goes to zero at an arbitrary rate eta(n). Both under the null and the alternative, we focus on rotationally symmetric distributions. We show that, while they are asymptotically equivalent under...
-
作者：Zhu, Ying
作者单位：Michigan State University
摘要：We consider a two-step projection based Lasso procedure for estimating a partially linear regression model where the number of coefficients in the linear component can exceed the sample size and these coefficients belong to the l(q) -balls for q is an element of [0, 1]. Our theoretical results regarding the properties of the estimators are nonasymptotic. In particular, we establish a new nonasymptotic oracle result: Although the error of the nonparametric projection per se (with respect to the...
-
作者：Jiang, Tiefeng; Leder, Kevin; Xu, Gongjun
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Minnesota System; University of Minnesota Twin Cities; University of Michigan System; University of Michigan
摘要：In this paper, we consider the extreme behavior of the extremal eigenvalues of white Wishart matrices, which plays an important role in multivariate analysis. In particular, we focus on the case when the dimension of the feature p is much larger than or comparable to the number of observations n, a common situation in modern data analysis. We provide asymptotic approximations and bounds for the tail probabilities of the extremal eigenvalues. Moreover, we construct efficient Monte Carlo simulat...
-
作者：Shi, Peibei; Qu, Annie
作者单位：University of Michigan System; University of Michigan; University of Illinois System; University of Illinois Urbana-Champaign
摘要：Weak signal identification and inference are very important in the area of penalized model selection, yet they are underdeveloped and not well studied. Existing inference procedures for penalized estimators are mainly focused on strong signals. In this paper, we propose an identification procedure for weak signals in finite samples, and provide a transition phase in-between noise and strong signal strengths. We also introduce a new two-step inferential method to construct better confidence int...
-
作者：Yang, Yun; Pilanci, Mert; Wainwright, Martin J.
作者单位：State University System of Florida; Florida State University; University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：Kernel ridge regression (KRR) is a standard method for performing non-parametric regression over reproducing kernel Hilbert spaces. Given n samples, the time and space complexity of computing the KRR estimate scale as O(n(3)) and O(n(2)), respectively, and so is prohibitive in many cases. We propose approximations of KRR based on m-dimensional randomized sketches of the kernel matrix, and study how small the projection dimension m can be chosen while still preserving minimax optimality of the ...
-
作者：Ghoshdastidar, Debarghya; Dukkipati, Ambedkar
作者单位：Indian Institute of Science (IISC) - Bangalore
摘要：Hypergraph partitioning lies at the heart of a number of problems in machine learning and network sciences. Many algorithms for hypergraph partitioning have been proposed that extend standard approaches for graph partitioning to the case of hypergraphs. However, theoretical aspects of such methods have seldom received attention in the literature as compared to the extensive studies on the guarantees of graph partitioning. For instance, consistency results of spectral graph partitioning under t...
-
作者：Datta, Abhirup; Zou, Hui
作者单位：Johns Hopkins University; University of Minnesota System; University of Minnesota Twin Cities
摘要：Much theoretical and applied work has been devoted to high-dimensional regression with clean data. However, we often face corrupted data in many applications where missing data and measurement errors cannot be ignored. Loh and Wainwright [Ann. Statist. 40 (2012) 1637-1664] proposed a non-convex modification of the Lasso for doing high-dimensional regression with noisy and missing data. It is generally agreed that the virtues of convexity contribute fundamentally the success and popularity of t...
-
作者：Ning, Yang; Zhao, Tianqi; Liu, Han
作者单位：Cornell University; Princeton University
摘要：We propose a new inferential framework for high-dimensional semiparametric generalized linear models. This framework addresses a variety of challenging problems in high-dimensional data analysis, including incomplete data, selection bias and heterogeneity. Our work has three main contributions: (i) We develop a regularized statistical chromatography approach to infer the parameter of interest under the proposed semiparametric generalized linear model without the need of estimating the unknown ...
-
作者：Pensky, Marianna
作者单位：State University System of Florida; University of Central Florida
摘要：The present paper considers the problem of estimating a linear functional Phi = integral(infinity)(-infinity) phi(x) f (x) dx of an unknown deconvolution density f on the basis of n i. i. d. observations, Y-1,..., Y-n of Y = theta +xi, where xi has a known pdf g, and f is the pdf of theta. The objective of the present paper is to develop the a general minimax theory of estimating Phi, and to relate this problem to estimation of functionals Phi(n) = n(-1) Sigma(n)(i=1) phi(theta(i)) in indirect...
-
作者：Dereudre, David; Lavancier, Frederic
作者单位：Universite de Lille; Nantes Universite
摘要：Strong consistency of the maximum likelihood estimator (MLE) for parametric Gibbs point process models is established. The setting is very general. It includes pairwise pair potentials, finite and infinite multibody interactions and geometrical interactions, where the range can be finite or infinite. The Gibbs interaction may depend linearly or nonlinearly on the parameters, a particular case being hardcore parameters and interaction range parameters. As important examples, we deduce the consi...
