2017

最新文章

• A GENERAL THEORY OF HYPOTHESIS TESTS AND CONFIDENCE REGIONS FOR SPARSE HIGH DIMENSIONAL MODELS AI翻译
  作者：Ning, Yang; Liu, Han
  作者单位：Cornell University; Princeton University
  摘要：We consider the problem of uncertainty assessment for low dimensional components in high dimensional models. Specifically, we propose a novel decorrelated score function to handle the impact of high dimensional nuisance parameters. We consider both hypothesis tests and confidence regions for generic penalized M-estimators. Unlike most existing inferential methods which are tailored for individual models, our method provides a general framework for high dimensional inference and is applicable t...
• NONPARAMETRIC CHANGE-POINT ANALYSIS OF VOLATILITY AI翻译
  作者：Bibinger, Markus; Jirak, Moritz; Vetter, Mathias
  作者单位：Braunschweig University of Technology; University of Kiel
  摘要：In this work, we develop change-point methods for statistics of highfrequency data. The main interest is in the volatility of an Ito semimartingale, the latter being discretely observed over a fixed time horizon. We construct a minimax-optimal test to discriminate continuous paths from paths with volatility jumps, and it is shown that the test can be embedded into a more general theory to infer the smoothness of volatilities. In a high-frequency setting, we prove weak convergence of the test s...
• ON COVERAGE AND LOCAL RADIAL RATES OF CREDIBLE SETS AI翻译
  作者：Belitser, Eduard
  作者单位：Vrije Universiteit Amsterdam
  摘要：In the mildly ill-posed inverse signal-in-white-noise model, we construct confidence sets as credible balls with respect to the empirical Bayes posterior resulting from a certain two-level hierarchical prior. The quality of the posterior is characterized by the contraction rate which we allow to be local, that is, depending on the parameter. The issue of optimality of the constructed confidence sets is addressed via a trade-off between its size (the local radial rate) and its coverage probabil...
• MINIMAX ESTIMATION OF LINEAR AND QUADRATIC FUNCTIONALS ON SPARSITY CLASSES AI翻译
  作者：Collier, Olivier; Comminges, Laetitia; Tsybakov, Alexandre B.
  作者单位：Universite Paris Saclay; Universite PSL; Universite Paris-Dauphine; Institut Polytechnique de Paris; ENSAE Paris
  摘要：For the Gaussian sequence model, we obtain nonasymptotic minimax rates of estimation of the linear, quadratic and the l(2)-norm functionals on classes of sparse vectors and construct optimal estimators that attain these rates. The main object of interest is the class B-0(s) of s-sparse vectors theta = (theta(1) (,...,) theta(d)), for which we also provide completely adaptive estimators (independent of s and of the noise variance sigma) having logarithmically slower rates than the minimax ones....
• SPARSE CCA: ADAPTIVE ESTIMATION AND COMPUTATIONAL BARRIERS AI翻译
  作者：Gao, Chao; Ma, Zongming; Zhou, Harrison H.
  作者单位：University of Chicago; University of Pennsylvania; Yale University
  摘要：Canonical correlation analysis is a classical technique for exploring the relationship between two sets of variables. It has important applications in analyzing high dimensional datasets originated from genomics, imaging and other fields. This paper considers adaptive minimax and computationally tractable estimation of leading sparse canonical coefficient vectors in high dimensions. Under a Gaussian canonical pair model, we first establish separate minimax estimation rates for canonical coeffi...
• BAYESIAN POISSON CALCULUS FOR LATENT FEATURE MODELING VIA GENERALIZED INDIAN BUFFET PROCESS PRIORS AI翻译
  作者：James, Lancelot F.
  作者单位：Hong Kong University of Science & Technology
  摘要：Statistical latent feature models, such as latent factor models, are models where each observation is associated with a vector of latent features. A general problem is how to select the number/types of features, and related quantities. In Bayesian statistical machine learning, one seeks (nonparametric) models where one can learn such quantities in the presence of observed data. The Indian Buffet Process (IBP), devised by Griffiths and Ghahramani (2005), generates a (sparse) latent binary matri...
• DETECTION AND FEATURE SELECTION IN SPARSE MIXTURE MODELS AI翻译
  作者：Verzelen, Nicolas; Arias-Castro, Ery
  作者单位：INRAE; University of California System; University of California San Diego
  摘要：We consider Gaussian mixture models in high dimensions, focusing on the twin tasks of detection and feature selection. Under sparsity assumptions on the difference in means, we derive minimax rates for the problems of testing and of variable selection. We find these rates to depend crucially on the knowledge of the covariance matrices and on whether the mixture is symmetric or not. We establish the performance of various procedures, including the top sparse eigenvalue of the sample covariance ...
• FUNCTIONAL CENTRAL LIMIT THEOREMS FOR SINGLE-STAGE SAMPLING DESIGNS AI翻译
  作者：Boistard, Helene; Lopuhaa, Hendrik P.; Ruiz-Gazen, Anne
  作者单位：Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Delft University of Technology
  摘要：For a joint model-based and design-based inference, we establish functional central limit theorems for the Horvitz-Thompson empirical process and the Hajek empirical process centered by their finite population mean as well as by their super-population mean in a survey sampling framework. The results apply to single-stage unequal probability sampling designs and essentially only require conditions on higher order correlations. We apply our main results to a Hadamard differentiable statistical f...
• YULE'S NONSENSE CORRELATION SOLVED! AI翻译
  作者：Ernst, Philip A.; Shepp, Larry A.; Wyner, Abraham J.
  作者单位：Rice University; University of Pennsylvania
  摘要：In this paper, we resolve a longstanding open statistical problem. The problem is to mathematically prove Yule's 1926 empirical finding of nonsense correlation [J. Roy. Statist. Soc. 89 (1926) 1-63], which we do by analytically determining the second moment of the empirical correlation coefficient theta : = integral(1)(0) W-1(t) W-2(t) dt - integral(1)(0) W-1(t) dt integral(1)(0) W-2(t) dt/root integral(1)(0) W-1(2)(t) dt - (integral(1)(0) W-1(t) dt)(2) root integral(1)(0) W-2(2)(t) dt - (inte...
• SUPPORT CONSISTENCY OF DIRECT SPARSE-CHANGE LEARNING IN MARKOV NETWORKS AI翻译
  作者：Liu, Song; Suzuki, Taiji; Relator, Raissa; Sese, Jun; Sugiyama, Masashi; Fukumizu, Kenji
  作者单位：Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan; Institute of Science Tokyo; Tokyo Institute of Technology; University of Tokyo; National Institute of Advanced Industrial Science & Technology (AIST)
  摘要：We study the problem of learning sparse structure changes between two Markov networks P and Q. Rather than fitting two Markov networks separately to two sets of data and figuring out their differences, a recent work proposed to learn changes directly via estimating the ratio between two Markov network models. In this paper, we give sufficient conditions for successful change detection with respect to the sample size n(p), n(q), the dimension of data m and the number of changed edges d. When us...