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作者：Jiang, Jiming; Li, Cong; Paul, Debashis; Yang, Can; Zhao, Hongyu
作者单位：University of California System; University of California Davis; Takeda Pharmaceutical Company Ltd; Takeda Pharmaceuticals International, Inc.; Hong Kong Baptist University; Yale University
摘要：We study behavior of the restricted maximum likelihood (REML) estimator under a misspecified linear mixed model (LMM) that has received much attention in recent genome-wide association studies. The asymptotic analysis establishes consistency of the REML estimator of the variance of the errors in the LMM, and convergence in probability of the REML estimator of the variance of the random effects in the LMM to a certain limit, which is equal to the true variance of the random effects multiplied b...
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作者：Chang, Jinyuan; Shao, Qi-Man; Zhou, Wen-Xin
作者单位：Southwestern University of Finance & Economics - China; University of Melbourne; Chinese University of Hong Kong; Princeton University
摘要：Two-sample U-statistics are widely used in a broad range of applications, including those in the fields of biostatistics and econometrics. In this paper, we establish sharp Cramer-type moderate deviation theorems for Studentized two-sample U-statistics in a general framework, including the two-sample t-statistic and Studentized Mann Whitney test statistic as prototypical examples. In particular, a refined moderate deviation theorem with second-order accuracy is established for the two-sample t...
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作者：Pillai, Natesh S.; Meng, Xiao-Li
作者单位：Harvard University
摘要：The Cauchy distribution is usually presented as a mathematical curiosity, an exception to the Law of Large Numbers, or even as an Evil distribution in some introductory courses. It therefore surprised us when Drton and Xiao [Bernoulli 22 (2016) 38-59] proved the following result for m = 2 and conjectured it for m >= 3. Let X = (X-1,...,X-m) and Y = (Y-1 ,...,Y-m) be i.i.d. N(0, Sigma), where Sigma = {sigma(ij)} >= 0 is an m x m and arbitrary covariance matrix with sigma(jj) > 0 for all 1 <= j ...
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作者：Akritas, Michael G.
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：For a response variable Y, and a d dimensional vector of covariates X, the first projective direction, V, is defined as the direction that accounts for the most variability in Y. The asymptotic distribution of an estimator of a trimmed version of V has been characterized only under the assumption of the single index model (SIM). This paper proposes the use of a flexible trimming function in the objective function, which results in the consistent estimation of V. It also derives the asymptotic ...
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作者：Li, Degui; Tjostheim, Dag; Gao, Jiti
作者单位：University of York - UK; University of Bergen; Monash University
摘要：In this paper, we study parametric nonlinear regression under the Harris recurrent Markov chain framework. We first consider the nonlinear least squares estimators of the parameters in the homoskedastic case, and establish asymptotic theory for the proposed estimators. Our results show that the convergence rates for the estimators rely not only on the properties of the nonlinear regression function, but also on the number of regenerations for the Harris recurrent Markov chain. Furthermore, we ...
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作者：Mueller, Hans-Georg
作者单位：University of California System; University of California Davis
摘要：Functional data analysis has become a major branch of nonparametric statistics and is a fast evolving field. Peter Hall has made fundamental contributions to this area and its theoretical underpinnings. He wrote more than 25 papers in functional data analysis between 1998 and 2016 and from 2005 on was a tenured faculty member with a 25% appointment in the Department of Statistics at the University of California, Davis. This article describes aspects of his appointment and academic life in Davi...
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作者：Cai, T. Tony; Li, Xiaodong; Ma, Zongming
作者单位：University of Pennsylvania; University of California System; University of California Davis
摘要：This paper considers the noisy sparse phase retrieval problem: recovering a sparse signal x is an element of R-P from noisy quadratic measurements y(j) = (a(j)'x)(2) + epsilon(j), j = 1,... m, with independent sub-exponential noise epsilon(j). The goals are to understand the effect of the sparsity of x on the estimation precision and to construct a computationally feasible estimator to achieve the optimal rates adaptively. Inspired by the Wirtinger Flow [IEEE Trans. Inform. Theory 61 (2015) 19...
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作者：Wang, Tengyao; Berthet, Quentin; Samworth, Richard J.
作者单位：University of Cambridge; California Institute of Technology
摘要：extremely popular dimension reduction technique for high-dimensional data. The theoretical challenge, in the simplest case, is to estimate the leading eigenvector of a population covariance matrix under the assumption that this eigenvector is sparse. An impressive range of estimators have been proposed; some of these are fast to compute, while others are known to achieve the mini-max optimal rate over certain Gaussian or sub-Gaussian classes. In this paper, we show that, under a widely-believe...
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作者：Cheng, Ming-Yen; Honda, Toshio; Li, Jialiang
作者单位：National Taiwan University; Hitotsubashi University; National University of Singapore
摘要：In semivarying coefficient modeling of longitudinal/clustered data, of primary interest is usually the parametric component which involves unknown constant coefficients. First, we study semiparametric efficiency bound for estimation of the constant coefficients in a general setup. It can be achieved by spline regression using the true within-subject covariance matrices, which are often unavailable in reality. Thus, we propose an estimator when the covariance matrices are unknown and depend onl...
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作者：Fan, Yingying; Lv, Jinchi
作者单位：University of Southern California
摘要：Large-scale precision matrix estimation is of fundamental importance yet challenging in many contemporary applications for recovering Gaussian graphical models. In this paper, we suggest a new approach of innovated scalable efficient estimation (ISEE) for estimating large precision matrix. Motivated by the innovated transformation, we convert the original problem into that of large covariance matrix estimation. The suggested method combines the strengths of recent advances in high-dimensional ...
