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作者：Bailey, R. A.; Brien, C. J.
作者单位：University of St Andrews; University of London; Queen Mary University London; University of South Australia; Australian Centre for Plant Functional Genomics; University of Adelaide
摘要：We derive randomization-based models for experiments with a chain of randomizations. Estimation theory for these models leads to formulae for the estimators of treatment effects, their standard errors and expected mean squares in the analysis of variance. We discuss the practicalities in fitting these models and outline the difficulties that can occur, many of which do not arise in two-tiered experiments.
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作者：Bertsimas, Dimitris; King, Angela; Mazumder, Rahul
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
摘要：In the period 1991-2015, algorithmic advances in Mixed Integer Optimization (MIO) coupled with hardware improvements have resulted in an astonishing 450 billion factor speedup in solving MIO problems. We present a MIO approach for solving the classical best subset selection problem of choosing k out of p features in linear regression given n observations. We develop a discrete extension of modern first-order continuous optimization methods to find high quality feasible solutions that we use as...
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作者：Bhattacharjee, Monika; Bose, Arup
作者单位：Indian Statistical Institute; Indian Statistical Institute Kolkata
摘要：The existence of limiting spectral distribution (LSD) of (Gamma) over cap (u) + (Gamma) over cap (u)*, the symmetric sum of the sample autocovariance matrix (Gamma) over cap (u) of order u, is known when the observations are from an infinite dimensional vector linear process with appropriate (strong) assumptions on the coefficient matrices. Under significantly weaker conditions, we prove, in a unified way, that the LSD of any symmetric polynomial in these matrices such as (Gamma) over cap (u) ...
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作者：Patschkowski, Tim; Rohde, Angelika
作者单位：Ruhr University Bochum
摘要：A scheme for locally adaptive bandwidth selection is proposed which sensitively shrinks the bandwidth of a kernel estimator at lowest density regions such as the support boundary which are unknown to the statistician. In case of a Holder continuous density, this locally minimax-optimal bandwidth is shown to be smaller than the usual rate, even in case of homogeneous smoothness. Some new type of risk bound with respect to a density-dependent standardized loss of this estimator is established. T...
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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：Song, Rui; Banerjee, Moulinath; Kosorok, Michael R.
作者单位：North Carolina State University; University of Michigan System; University of Michigan; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina; University of North Carolina Chapel Hill
摘要：Change-point models are widely used by statisticians to model drastic changes in the pattern of observed data. Least squares/maximum likelihood based estimation of change-points leads to curious asymptotic phenomena. When the change-point model is correctly specified, such estimates generally converge at a fast rate (n) and are asymptotically described by minimizers of a jump process. Under complete mis-specification by a smooth curve, that is, when a change-point model is fitted to data descr...
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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：Cai, T. Tony; Liang, Tengyuan; Rakhlin, Alexander
作者单位：University of Pennsylvania
摘要：This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix estimation and noisy matrix completion. We propose computationally feasible convex programs for statistical inference including estimation, confidence intervals and hypothesis testing. A theoretical framework is developed to characterize the local estimation ...
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作者：Chen, Xiaohong; Shao, Qi-Man; Wu, Wei Biao; Xu, Lihu
作者单位：Yale University; Chinese University of Hong Kong; University of Chicago; University of Macau
摘要：We establish a Cramer-type moderate deviation result for self-normalized sums of weakly dependent random variables, where the moment requirement is much weaker than the non-self-normalized counterpart. The range of the moderate deviation is shown to depend on the moment condition and the degree of dependence of the underlying processes. We consider three types of self-normalization: the equal-block scheme, the big-block-small-block scheme and the interlacing scheme. Simulation study shows that...
