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作者：Chen, S.; Dick, J.; Owen, A. B.
作者单位：Stanford University; University of New South Wales Sydney
摘要：The random numbers driving Markov chain Monte Carlo (MCMC) simulation are usually modeled as independent U(0, 1) random variables. Tribble [Markov chain Monte Carlo algorithms using completely uniformly distributed driving sequences (2007) Stanford Univ.] reports substantial improvements when those random numbers are replaced by carefully balanced inputs from completely uniformly distributed sequences. The previous theoretical justification for using anything other than lid. U(0, 1) points sho...
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作者：Zhang, Runchu; Phoa, Frederick K. H.; Mukerjee, Rahul; Xu, Hongquan
作者单位：Nankai University; Nankai University; Indian Institute of Management (IIM System); Indian Institute of Management Calcutta; University of California System; University of California Los Angeles; Academia Sinica - Taiwan; Northeast Normal University - China
摘要：The study of good nonregular fractional factorial designs has received significant attention over the last two decades. Recent research indicates that designs constructed from quaternary codes (QC) are very promising in this regard. The present paper shows how a trigonometric approach can facilitate a systematic understanding of such QC designs and lead to new theoretical results covering hitherto unexplored situations. We focus attention on one-eighth and one-sixteenth fractions of two-level ...
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作者：Atchade, Yves F.
作者单位：University of Michigan System; University of Michigan
摘要：We study the asymptotic behavior of kernel estimators of asymptotic variances (or long-run variances) for a class of adaptive Markov chains. The convergence is studied both in L-P and almost surely. The results also apply to Markov chains and improve on the existing literature by imposing weaker conditions. We illustrate the results with applications to the GARCH(1, 1) Markov model and to an adaptive MCMC algorithm for Bayesian logistic regression.
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作者：Duembgen, Lutz; Samworth, Richard; Schuhmacher, Dominic
作者单位：University of Bern; University of Cambridge
摘要：We study the approximation of arbitrary distributions P on d-dimensional space by distributions with log-concave density. Approximation means minimizing a Kullback Leibler-type functional. We show that such an approximation exists if and only if P has finite first moments and is not supported by some hyperplane. Furthermore we show that this approximation depends continuously on P with respect to Mallows distance D-1(.,.). This result implies consistency of the maximum likelihood estimator of ...
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作者：Kerkyacharian, Gerard; Thanh Mai Pham Ngoc; Picard, Dominique
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite
摘要：We provide a new algorithm for the treatment of the deconvolution problem on the sphere which combines the traditional SVD inversion with an appropriate thresholding technique in a well chosen new basis. We establish upper bounds for the behavior of our procedure for any L-p loss. It is important to emphasize the adaptation properties of our procedures with respect to the regularity (sparsity) of the object to recover as well as to inhomogeneous smoothness. We also perform a numerical study wh...
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作者：Sun, Fasheng; Lin, Dennis K. J.; Liu, Min-Qian
作者单位：Northeast Normal University - China; Northeast Normal University - China; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Nankai University; Nankai University
摘要：Supersaturated design (SSD) has received much recent interest because of its potential in factor screening experiments. In this paper, we provide equivalent conditions for two columns to be fully aliased and consequently propose methods for constructing E(f(NoD))- and chi(2)-optimal mixed-level SSDs without fully aliased columns, via equidistant designs and difference matrices. The methods can be easily performed and many new optimal mixed-level SSDs have been obtained. Furthermore, it is prov...
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作者：Comte, Fabienne; Genon-Catalot, Valentine
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis
摘要：In this paper, we study nonparametric estimation of the Levy density for Levy processes, with and without Brownian component. For this, we consider n discrete time observations with step Delta. The asymptotic framework is: n tends to infinity, Delta = Delta(n), tends to zero while n Delta(n) tends to infinity. We use a Fourier approach to construct an adaptive nonparametric estimator of the Levy density and to provide a bound for the global L-2-risk. Estimators of the drift and of the variance...
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作者：Bacallado, Sergio
作者单位：Stanford University
摘要：We define a conjugate prior for the reversible Markov chain of order r. The prior arises from a partially exchangeable reinforced random walk, in the same way that the Beta distribution arises from the exchangeable Polya urn. An extension to variable-order Markov chains is also derived. We show the utility of this prior in testing the order and estimating the parameters of a reversible Markov model.
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作者：Shao, Jun; Wang, Yazhen; Deng, Xinwei; Wang, Sijian
作者单位：East China Normal University; University of Wisconsin System; University of Wisconsin Madison
摘要：In many social, economical, biological and medical studies, one objective is to classify a subject into one of several classes based on a set of variables observed from the subject. Because the probability distribution of the variables is usually unknown, the rule of classification is constructed using a training sample. The well-known linear discriminant analysis (LDA) works well for the situation where the number of variables used for classification is much smaller than the training sample s...
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作者：Tang, Runlong; Banerjee, Moulinath; Michailidis, George
作者单位：University of Michigan System; University of Michigan
摘要：We consider a two-stage procedure (TSP) for estimating an inverse regression function at a given point, where isotonic regression is used at stage one to obtain an initial estimate and a local linear approximation in the vicinity of this estimate is used at stage two. We establish that the convergence rate of the second-stage estimate can attain the parametric n(1/2) rate. Furthermore, a bootstrapped variant of TSP (BTSP) is introduced and its consistency properties studied. This variant manag...
