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作者：Lockhart, Richard; Taylor, Jonathan; Tibshirani, Ryan J.; Tibshirani, Robert
作者单位：Simon Fraser University; Stanford University; Carnegie Mellon University; Carnegie Mellon University; Stanford University
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作者：Maire, Florian; Douc, Randal; Olsson, Jimmy
作者单位：IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; Royal Institute of Technology
摘要：In this paper, we study the asymptotic variance of sample path averages for inhomogeneous Markov chains that evolve alternatingly according to two different 7-reversible Markov transition kernels P and Q. More specifically, our main result allows us to compare directly the asymptotic variances of two inhomogeneous Markov chains associated with different kernels Pi and Q(i), i is an element of {0, 1}, as soon as the kernels of each pair (P-0, P-1) and (Q(0), Q(1)) can be ordered in the sense of...
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作者：Schmidt-Hieber, Johannes
作者单位：Leiden University - Excl LUMC; Leiden University
摘要：Consider estimation of the regression function based on a model with equidistant design and measurement errors generated from a fractional Gaussian noise process. In previous literature, this model has been heuristically linked to an experiment, where the anti-derivative of the regression function is continuously observed under additive perturbation by a fractional Brownian motion. Based on a reformulation of the problem using reproducing kernel Hilbert spaces, we derive abstract approximation...
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作者：Cheng, Ming-Yen; Honda, Toshio; Li, Jialiang; Peng, Heng
作者单位：National Taiwan University; Hitotsubashi University; National University of Singapore; Hong Kong Baptist University
摘要：Ultra-high dimensional longitudinal data are increasingly common and the analysis is challenging both theoretically and methodologically. We offer a new automatic procedure for finding a sparse semivarying coefficient model, which is widely accepted for longitudinal data analysis. Our proposed method first reduces the number of covariates to a moderate order by employing a screening procedure, and then identifies both the varying and constant coefficients using a group SCAD estimator, which is...
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作者：Lockhart, Richard; Taylor, Jonathan; Tibshirani, Ryan J.; Tibshirani, Robert
作者单位：Simon Fraser University; Stanford University; Carnegie Mellon University; Stanford University
摘要：In the sparse linear regression setting, we consider testing the significance of the predictor variable that enters the current lasso model, in the sequence of models visited along the lasso solution path. We propose a simple test statistic based on lasso fitted values, called the covariance test statistic, and show that when the true model is linear, this statistic has an Exp(1) asymptotic distribution under the null hypothesis (the null being that all truly active variables are contained in ...
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作者：Szekely, Gabor J.; Rizzo, Maria L.
作者单位：National Science Foundation (NSF); University System of Ohio; Bowling Green State University
摘要：Distance covariance and distance correlation are scalar coefficients that characterize independence of random vectors in arbitrary dimension. Properties, extensions and applications of distance correlation have been discussed in the recent literature, but the problem of defining the partial distance correlation has remained an open question of considerable interest. The problem of partial distance correlation is more complex than partial correlation partly because the squared distance covarian...
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作者：Yoshimori, Masayo; Lahiri, Partha
作者单位：University of Osaka; University System of Maryland; University of Maryland College Park
摘要：We introduce a new adjusted residual maximum likelihood method (REML) in the context of producing an empirical Bayes (EB) confidence interval for a normal mean, a problem of great interest in different small area applications. Like other rival empirical Bayes confidence intervals such as the well-known parametric bootstrap empirical Bayes method, the proposed interval is second-order correct, that is, the proposed interval has a coverage error of order O(m(-3/2)). Moreover, the proposed interv...
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作者：Jankowski, Hanna
作者单位：York University - Canada
摘要：Under the assumption that the true density is decreasing, it is well known that the Grenander estimator converges at rate n(1/3) if the true density is curved [Sankhya Ser. A 31 (1969) 23-36] and at rate n(1/2) if the density is flat [Ann. Probab. 11 (1983) 328-345; Canad. J. Statist. 27 (1999) 557-566]. In the case that the true density is misspecified, the results of Patilea [Ann. Statist. 29 (2001) 94-123] tell us that the global convergence rate is of order n1/3 in Hellinger distance. Here...
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作者：Buecher, Axel; Segers, Johan; Volgushev, Stanislav
作者单位：Ruhr University Bochum; Universite Catholique Louvain
摘要：In the past decades, weak convergence theory for stochastic processes has become a standard tool for analyzing the asymptotic properties of various statistics. Routinely, weak convergence is considered in the space of bounded functions equipped with the supremum metric. However, there are cases when weak convergence in those spaces fails to hold. Examples include empirical copula and tail dependence processes and residual empirical processes in linear regression models in case the underlying d...
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作者：Groemping, Ulrike; Xu, Hongquan
作者单位：University of California System; University of California Los Angeles
摘要：The generalized word length pattern of an orthogonal array allows a ranking of orthogonal arrays in terms of the generalized minimum aberration criterion (Xu and Wu [Ann. Statist. 29 (2001) 1066-1077]). We provide a statistical interpretation for the number of shortest words of an orthogonal array in terms of sums of R-2 values (based on orthogonal coding) or sums of squared canonical correlations (based on arbitrary coding). Directly related to these results, we derive two versions of general...
