-
作者：Vu, Vincent Q.; Lei, Jing
作者单位：University System of Ohio; Ohio State University; Carnegie Mellon University
摘要：We study sparse principal components analysis in high dimensions, where p (the number of variables) can be much larger than n (the number of observations), and analyze the problem of estimating the subspace spanned by the principal eigenvectors of the population covariance matrix. We introduce two complementary notions of eq subspace sparsity: row sparsity and column sparsity. We prove nonasymptotic lower and upper bounds on the minimax subspace estimation error for 0 <= q <= I. The bounds are...
-
作者：Dette, Holger; Melas, Viatcheslav B.; Shpilev, Petr
作者单位：Ruhr University Bochum; Saint Petersburg State University
摘要：This paper considers the problem of constructing optimal discriminating experimental designs for competing regression models on the basis of the T-optimality criterion introduced by Atkinson and Fedorov [Biometrika 62 (1975a) 57-70]. T-optimal designs depend on unknown model parameters and it is demonstrated that these designs are sensitive with respect to misspecification. As a solution to this problem we propose a Bayesian and standardized maximin approach to construct robust and efficient d...
-
作者：Zhang, Li
作者单位：Microsoft
摘要：We present estimators for a well studied statistical estimation problem: the estimation for the linear regression model with soft sparsity constraints (lq constraint with 0 <= 1) in the high-dimensional setting. We first present a family of estimators, called the projected nearest neighbor estimator and show, by using results from Convex Geometry, that such estimator is within a logarithmic factor of the optimal for any design matrix. Then by utilizing a semi-definite programming relaxation te...
-
作者：Lee, Kuang-Yao; Li, Bing; Chiaromonte, Francesca
作者单位：Yale University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：In this paper we introduce a general theory for nonlinear sufficient dimension reduction, and explore its ramifications and scope. This theory subsumes recent work employing reproducing kernel Hilbert spaces, and reveals many parallels between linear and nonlinear sufficient dimension reduction. Using these parallels we analyze the properties of existing methods and develop new ones. We begin by characterizing dimension reduction at the general level of sigma-fields and proceed to that of clas...
-
作者：Woodard, Dawn B.; Rosenthal, Jeffrey S.
作者单位：Cornell University; Cornell University; University of Toronto
摘要：We analyze the convergence rate of a simplified version of a popular Gibbs sampling method used for statistical discovery of gene regulatory binding motifs in DNA sequences. This sampler satisfies a very strong form of ergodicity (uniform). However, we show that, due to multimodality of the posterior distribution, the rate of convergence often decreases exponentially as a function of the length of the DNA sequence. Specifically, we show that this occurs whenever there is more than one true rep...
-
作者：Hall, Peter; Horowitz, Joel
作者单位：University of Melbourne; University of California System; University of California Davis; Northwestern University
摘要：Standard approaches to constructing nonparametric confidence bands for functions are frustrated by the impact of bias, which generally is not estimated consistently when using the bootstrap and conventionally smoothed function estimators. To overcome this problem it is common practice to either undersmooth, so as to reduce the impact of bias, or oversmooth, and thereby introduce an explicit or implicit bias estimator. However, these approaches, and others based on nonstandard smoothing methods...
-
作者：Dette, Holger; Schorning, Kirsten
作者单位：Ruhr University Bochum
摘要：In a recent paper Yang and Stufken [Ann. Statist. 40 (2012a) 1665-1685] gave sufficient conditions for complete classes of designs for nonlinear regression models. In this note we demonstrate that there is an alternative way to validate this result. Our main argument utilizes the fact that boundary points of moment spaces generated by Chebyshev systems possess unique representations.
-
作者：Jacod, Jean; Rosenbaum, Mathieu
作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite
摘要：We consider a multidimensional Ito semimartingale regularly sampled on [0, t] at high frequency 1/Delta(n), with Delta(n) going to zero. The goal of this paper is to provide an estimator for the integral over [0, t] of a given function of the volatility matrix. To approximate the integral, we simply use a Riemann sum based on local estimators of the pointwise volatility. We show that although the accuracy of the pointwise estimation is at most Delta(1/4)(n), this procedure reaches the parametr...
-
作者：Suzuki, Taiji; Sugiyama, Masashi
作者单位：University of Tokyo; Institute of Science Tokyo; Tokyo Institute of Technology
摘要：We investigate the learning rate of multiple kernel learning (MKL) with l(1) and elastic-net regularizations. The elastic-net regularization is a composition of an l(1)-regularizer for inducing the sparsity and an l(2)-regularizer for controlling the smoothness. We focus on a sparse setting where the total number of kernels is large, but the number of nonzero components of the ground truth is relatively small, and show sharper convergence rates than the learning rates have ever shown for both ...
-
作者：Bull, Adam D.
作者单位：University of Cambridge
摘要：While adaptive sensing has provided improved rates of convergence in sparse regression and classification, results in nonparametric regression have so far been restricted to quite specific classes of functions. In this, paper, we describe an adaptive-sensing algorithm which is applicable to general nonparametric-regression problems. The algorithm is spatially adaptive, and achieves improved rates of convergence over spatially inhomogeneous functions. Over standard function classes, it likewise...
