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作者：Ghosh, Swarnadip; Hastie, Trevor; Owen, Art B.
作者单位：Stanford University
摘要：Regression models with crossed random effect errors can be very expensive to compute. The cost of both generalized least squares and Gibbs sampling can easily grow as N-3/2 (or worse) for N observations. Papaspiliopoulos, Roberts and Zanella (Biometrika 107 (2020) 25-40) present a collapsed Gibbs sampler that costs O(N), but under an extremely stringent sampling model. We propose a backfitting algorithm to compute a generalized least squares estimate and prove that it costs O(N). A critical pa...
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作者：Huang, Jianhua Z.; Su, Ya
作者单位：Texas A&M University System; Texas A&M University College Station; Virginia Commonwealth University
摘要：This paper develops a general theory on rates of convergence of penalized spline estimators for function estimation when the likelihood functional is concave in candidate functions, where the likelihood is interpreted in a broad sense that includes conditional likelihood, quasi-likelihood and pseudo-likelihood. The theory allows all feasible combinations of the spline degree, the penalty order and the smoothness of the unknown functions. According to this theory, the asymptotic behaviors of th...
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作者：Kwon, Caleb; Mbakop, Eric
作者单位：Harvard University; University of Calgary
摘要：We propose a novel estimator for the number of mixture components (denoted by M) in a nonparametric finite mixture model. The setting that we consider is one where the analyst has repeated observations of K >= 2 variables that are conditionally independent given a finitely supported latent variable withM support points. Under a mild assumption on the joint distribution of the observed and latent variables, we show that an integral operator T that is identified from the data has rank equal to M...
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作者：del Alamo, Miguel; Li, Housen; Munk, Axel
作者单位：University of Gottingen
摘要：Despite the popularity and practical success of total variation (TV) regularization for function estimation, surprisingly little is known about its theoretical performance in a statistical setting. While TV regularization has been known for quite some time to be minimax optimal for denoising one-dimensional signals, for higher dimensions this remains elusive until today. In this paper, we consider frame-constrained TV estimators including many well-known (overcomplete) frames in a white noise ...
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作者：Camerlenghi, Federico; Favaro, Stefano; Naulet, Zacharie; Panero, Francesca
作者单位：University of Milano-Bicocca; University of Turin; Universite Paris Saclay; University of Oxford
摘要：Protection against disclosure is a legal and ethical obligation for agencies releasing microdata files for public use. Consider a microdata sample of size n from a finite population of size (n) over bar n = n + lambda n, with lambda > 0, such that each sample record contains two disjoint types of information: identifying categorical information and sensitive information. Any decision about releasing data is supported by the estimation of measures of disclosure risk, which are defined as discre...
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作者：Freise, Fritjof; Gaffke, Norbert; Schwabe, Rainer
作者单位：University of Veterinary Medicine Hannover; Otto von Guericke University
摘要：For a nonlinear regression model, the information matrices of designs depend on the parameter of the model. The adaptive Wynn algorithm for D-optimal design estimates the parameter at each step on the basis of the observed responses and employed design points so far, and selects the next design point as in the classicalWynn algorithm for D-optimal design. The name Wynn algorithm is in honor of Henry P. Wynn who established the latter classical algorithm in his 1970 paper (Ann. Math. Stat. 41 (...
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作者：She, Yiyuan; Wang, Zhifeng; Jin, Jiuwu
作者单位：State University System of Florida; Florida State University
摘要：Modern statistical applications often involve minimizing an objective function that may be nonsmooth and/or nonconvex. This paper focuses on a broad Bregman-surrogate algorithm framework including the local linear approximation, mirror descent, iterative thresholding, DC programming and many others as particular instances. The recharacterization via generalized Bregman functions enables us to construct suitable error measures and establish global convergence rates for nonconvex and nonsmooth o...
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作者：Berrett, Thomas B.; Kontoyiannis, Ioannis; Samworth, Richard J.
作者单位：University of Warwick; University of Cambridge
摘要：We study the problem of independence testing given independent and identically distributed pairs taking values in a sigma-finite, separable measure space. Defining a natural measure of dependence D(f) as the squared L-2 distance between a joint density f and the product of its marginals, we first show that there is no valid test of independence that is uniformly consistent against alternatives of the form {f : D(f) >= rho(2) }. We therefore restrict attention to alternatives that impose additi...
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作者：Samworth, Richard J.; Yuan, Ming
作者单位：University of Cambridge; Columbia University
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作者：Cai, Changxiao; Li, Gen; Chi, Yuejie; Poor, H. Vincent; Chen, Yuxin
作者单位：Princeton University; Tsinghua University; Carnegie Mellon University
摘要：This paper is concerned with estimating the column space of an unknown low-rank matrix A(star) is an element of R-d1xd2, given noisy and partial observations of its entries. There is no shortage of scenarios where the observations-while being too noisy to support faithful recovery of the entire matrix-still convey sufficient information to enable reliable estimation of the column space of interest. This is particularly evident and crucial for the highly unbalanced case where the column dimensi...
