-
作者：Choi, David; Wolfe, Patrick J.
作者单位：Carnegie Mellon University; University of London; University College London
摘要：This article establishes the performance of stochastic blockmodels in addressing the co-clustering problem of partitioning a binary array into subsets, assuming only that the data are generated by a nonparametric process satisfying the condition of separate exchangeability. We provide oracle inequalities with rate of convergence O-P(n(-1/4)) corresponding to profile likelihood maximization and mean-square error minimization, and show that the blockmodel can be interpreted in this setting as an...
-
作者：Tibshirani, Ryan J.
作者单位：Carnegie Mellon University
摘要：We study trend filtering, a recently proposed tool of Kim et al. [SIAM Rev. 51 (2009) 339-360] for nonparametric regression. The trend filtering estimate is defined as the minimizer of a penalized least squares criterion, in which the penalty term sums the absolute kth order discrete derivatives over the input points. Perhaps not surprisingly, trend filtering estimates appear to have the structure of kth degree spline functions, with adaptively chosen knot points (we say appear here as trend f...
-
作者：McElroy, Tucker S.; Holan, Scott H.
作者单位：University of Missouri System; University of Missouri Columbia
摘要：Random fields play a central role in the analysis of spatially correlated data and, as a result, have a significant impact on a broad array of scientific applications. This paper studies the cepstral random field model, providing recursive formulas that connect the spatial cepstral coefficients to an equivalent moving-average random field, which facilitates easy computation of the autocovariance matrix. We also provide a comprehensive treatment of the asymptotic theory for two-dimensional rand...
-
作者：Onatski, Alexei; Moreira, Marcelo J.; Hallin, Marc
作者单位：University of Cambridge; Getulio Vargas Foundation; Universite Libre de Bruxelles; Princeton University
摘要：This paper applies Le Cam's asymptotic theory of statistical experiments to the signal detection problem in high dimension. We consider the problem of testing the null hypothesis of sphericity of a high-dimensional covariance matrix against an alternative of (unspecified) multiple symmetry-breaking directions (multispiked alternatives). Simple analytical expressions for the Gaussian asymptotic power envelope and the asymptotic powers of previously proposed tests are derived. Those asymptotic p...
-
作者：Feng, Xingdong; He, Xuming
作者单位：Shanghai University of Finance & Economics; Shanghai University of Finance & Economics; University of Michigan System; University of Michigan
摘要：The singular value decomposition is widely used to approximate data matrices with lower rank matrices. Feng and He [Ann. Appl. Stat. 3 (2009) 1634-1654] developed tests on dimensionality of the mean structure of a data matrix based on the singular value decomposition. However, the first singular values and vectors can be driven by a small number of outlying measurements. In this paper, we consider a robust alternative that moderates the effect of outliers in low-rank approximations. Under the ...
-
作者：Lecue, Guillaume; Rigollet, Philippe
作者单位：Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique; Princeton University
摘要：We consider a general supervised learning problem with strongly convex and Lipschitz loss and study the problem of model selection aggregation. In particular, given a finite dictionary functions (learners) together with the prior, we generalize the results obtained by Dai, Rigollet and Zhang [Ann. Statist. 40 (2012) 1878-1905] for Gaussian regression with squared loss and fixed design to this learning setup. Specifically, we prove that the Q-aggregation procedure outputs an estimator that sati...
-
作者：Fan, Jianqing; Fan, Yingying; Barut, Emre
作者单位：Princeton University; University of Southern California; International Business Machines (IBM); IBM USA
摘要：Heavy-tailed high-dimensional data are commonly encountered in various scientific fields and pose great challenges to modern statistical analysis. A natural procedure to address this problem is to use penalized quantile regression with weighted L-1-penalty, called weighted robust Lasso (WR-Lasso), in which weights are introduced to ameliorate the bias problem induced by the L-1-penalty. In the ultra-high dimensional setting, where the dimensionality can grow exponentially with the sample size,...
-
作者：Bhattacharya, Anirban; Pati, Debdeep; Dunson, David
作者单位：Texas A&M University System; Texas A&M University College Station; State University System of Florida; Florida State University; Duke University
摘要：In nonparametric regression problems involving multiple predictors, there is typically interest in estimating an anisotropic multivariate regression surface in the important predictors while discarding the unimportant ones. Our focus is on defining a Bayesian procedure that leads to the minimax optimal rate of posterior contraction (up to a log factor) adapting to the unknown dimension and anisotropic smoothness of the true surface. We propose such an approach based on a Gaussian process prior...
-
作者：Luo, Wei; Li, Bing; Yin, Xiangrong
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; University System of Georgia; University of Georgia
摘要：We introduce a new sufficient dimension reduction framework that targets a statistical functional of interest, and propose an efficient estimator for the semiparametric estimation problems of this type. The statistical functional covers a wide range of applications, such as conditional mean, conditional variance and conditional quantile. We derive the general forms of the efficient score and efficient information as well as their specific forms for three important statistical functionals: the ...
-
作者：Li, Ke
作者单位：International Business Machines (IBM); IBM USA; Massachusetts Institute of Technology (MIT); National University of Singapore
摘要：In the asymptotic theory of quantum hypothesis testing, the minimal error probability of the first kind jumps sharply from zero to one when the error exponent of the second kind passes by the point of the relative entropy of the two states in an increasing way. This is well known as the direct part and strong converse of quantum Stein's lemma. Here we look into the behavior of this sudden change and have make it clear how the error of first kind grows smoothly according to a lower order of the...
