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作者：Zhu, Guangyu; Su, Zhihua
作者单位：University of Rhode Island; State University System of Florida; University of Florida
摘要：Sparse partial least squares (SPLS) is widely used in applied sciences as a method that performs dimension reduction and variable selection simultaneously in linear regression. Several implementations of SPLS have been derived, among which the SPLS proposed in Chun and Keles (J. R. Stat. Soc. Ser. B. Stat. Methodol. 72 (2010) 3-25) is very popular and highly cited. However, for all of these implementations, the theoretical properties of SPLS are largely unknown. In this paper, we propose a new...
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作者：Ing, Ching-Kang
作者单位：National Tsing Hua University
摘要：We investigate the prediction capability of the orthogonal greedy algorithm (OGA) in high-dimensional regression models with dependent observations. The rates of convergence of the prediction error of OGA are obtained under a variety of sparsity conditions. To prevent OGA from overfitting, we introduce a high-dimensional Akaike's information criterion (HDAIC) to determine the number of OGA iterations. A key contribution of this work is to show that OGA, used in conjunction with HDAIC, can achi...
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作者：Zhang, Fengshuo; Gao, Chao
作者单位：University of Chicago
摘要：We study convergence rates of variational posterior distributions for non-parametric and high-dimensional inference. We formulate general conditions on prior, likelihood and variational class that characterize the convergence rates. Under similar prior mass and testing conditions considered in the literature, the rate is found to be the sum of two terms. The first term stands for the convergence rate of the true posterior distribution, and the second term is contributed by the variational appr...
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作者：Giordano, Francesco; Lahiri, Soumendra Nath; Parrella, Maria Lucia
作者单位：University of Salerno; North Carolina State University
摘要：We consider nonparametric regression in high dimensions where only a relatively small subset of a large number of variables are relevant and may have nonlinear effects on the response. We develop methods for variable selection, structure discovery and estimation of the true low-dimensional regression function, allowing any degree of interactions among the relevant variables that need not be specified a-priori. The proposed method, called the GRID, combines empirical likelihood based marginal t...
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作者：Ekvall, Karl Oskar; Jones, Galin L.
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We present new results for consistency of maximum likelihood estimators with a focus on multivariate mixed models. Our theory builds on the idea of using subsets of the full data to establish consistency of estimators based on the full data. It requires neither that the data consist of independent observations, nor that the observations can be modeled as a stationary stochastic process. Compared to existing asymptotic theory using the idea of subsets, we substantially weaken the assumptions, b...
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作者：Ghosal, Promit; Mukherjee, Sumit
作者单位：Columbia University
摘要：We study joint estimation of the inverse temperature and magnetization parameters (beta, B) of an Ising model with a nonnegative coupling matrix A(n) of size n x n, given one sample from the Ising model. We give a general bound on the rate of consistency of the bi-variate pseudo-likelihood estimator. Using this, we show that estimation at rate n(-1/2) is always possible if A(n) is the adjacency matrix of a bounded degree graph. If A(n) is the scaled adjacency matrix of a graph whose average de...
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作者：Bravo, Francesco; Carlos Escanciano, Juan; Van Keilegom, Ingrid
作者单位：University of York - UK; Universidad Carlos III de Madrid; KU Leuven
摘要：In both parametric and certain nonparametric statistical models, the empirical likelihood ratio satisfies a nonparametric version of Wilks' theorem. For many semiparametric models, however, the commonly used two-step (plug-in) empirical likelihood ratio is not asymptotically distribution-free, that is, its asymptotic distribution contains unknown quantities, and hence Wilks' theorem breaks down. This article suggests a general approach to restore Wilks' phenomenon in two-step semiparametric em...
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作者：Shi, Chengchun; Song, Rui; Chen, Zhao; Li, Runze
作者单位：North Carolina State University; Fudan University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：This paper is concerned with testing linear hypotheses in high dimensional generalized linear models. To deal with linear hypotheses, we first propose the constrained partial regularization method and study its statistical properties. We further introduce an algorithm for solving regularization problems with folded-concave penalty functions and linear constraints. To test linear hypotheses, we propose a partial penalized likelihood ratio test, a partial penalized score test and a partial penal...
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作者：Ierkens, Joris B.; Fearnhead, Paul; Roberts, Gareth
作者单位：Delft University of Technology; Delft University of Technology; Lancaster University; University of Warwick
摘要：Standard MCMC methods can scale poorly to big data settings due to the need to evaluate the likelihood at each iteration. There have been a number of approximate MCMC algorithms that use sub-sampling ideas to reduce this computational burden, but with the drawback that these algorithms no longer target the true posterior distribution. We introduce a new family of Monte Carlo methods based upon a multidimensional version of the Zig-Zag process of [Ann. Appl. Probab. 27 (2017) 846-882], a contin...
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作者：Banerjee, Moulinath; Durot, Cecile; Sen, Bodhisattva
作者单位：University of Michigan System; University of Michigan; Columbia University
摘要：We study how the divide and conquer principle works in non-standard problems where rates of convergence are typically slower than root n and limit distributions are non-Gaussian, and provide a detailed treatment for a variety of important and well-studied problems involving nonparametric estimation of a monotone function. We find that for a fixed model, the pooled estimator, obtained by averaging nonstandard estimates across mutually exclusive subsamples, outperforms the nonstandard monotonici...
