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作者：Davies, P. Laurie; Gather, Ursula
作者单位：University of Duisburg Essen; Dortmund University of Technology
摘要：In his discussion of Davies and Gather [Ann. Statist. 33 (2005) 977-1035] Tyler pointed out that the theory developed there could not be applied to the case of directional data. He related the breakdown of directional functionals to the problem of definability. In this addendum we provide a concept of breakdown defined in terms of definability and not in terms of bias. If a group of finite order k acts on the sample space we show that the breakdown point can be bounded above by (k - 1)/k. In t...
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作者：Gardner, Richard J.; Kiderlen, Markus; Milanfar, Peyman
作者单位：Western Washington University; Aarhus University; University of California System; University of California Santa Cruz
摘要：We investigate algorithms for reconstructing a convex body K in R-n from noisy measurements of its support function or its brightness function in k directions u(1), (. .) (.) , u(k). The key idea of these algorithms is to construct a convex polytope P-k whose support function (or brightness function) best approximates the given measurements in the directions u(1), (.) (.) (.) , u(k) (in the least squares sense). The measurement errors are assumed to be stochastically independent and Gaussian. ...
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作者：Buhlmann, Peter
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We prove that boosting with the squared error loss, L(2)Boosting, is consistent for very high-dimensional linear models, where the number of predictor variables is allowed to grow essentially as fast as O(exp(sample size)), assuming that the true underlying regression function is sparse in terms of the l(1)-norm of the regression coefficients. In the language of signal processing, this means consistency for de-noising using a strongly overcomplete dictionary if the underlying signal is sparse ...
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作者：Csorgo, Miklos; Szyszkowicz, Barbara; Wang, Lihong
作者单位：Carleton University; Nanjing University
摘要：In this paper we study strong approximations (invariance principles) of the sequential uniform and general Bahadur-Kiefer processes of long-range dependent sequences. We also investigate the strong and weak asymptotic behavior of the sequential Vervaat process, that is, the integrated sequential Bahadur-Kiefer process, properly normalized, as well as that of its deviation from its limiting process, the so-called Vervaat error process. It is well known that the Bahadur-Kiefer and the Vervaat er...
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作者：Koul, Hira L.; Ling, Shiqing
作者单位：Michigan State University; Hong Kong University of Science & Technology
摘要：This paper addresses the problem of fitting a known distribution to the innovation distribution in a class of stationary and ergodic time series models. The asymptotic null distribution of the usual Kolmogorov-Smimov test based on the residuals generally depends on the underlying model parameters and the error distribution. To overcome the dependence on the underlying model parameters, we propose that tests be based on a vector of certain weighted residual empirical processes. Under the null h...
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作者：Zu, Yijun; He, Xuming
作者单位：Michigan State University; University of Illinois System; University of Illinois Urbana-Champaign
摘要：A depth-based rank sum statistic for multivariate data introduced by Liu and Singh [J. Amer. Statist. Assoc. 88 (1993) 252-260] as an extension of the Wilcoxon rank sum statistic for univariate data has been used in multivariate rank tests in quality control and in experimental studies. Those applications, however, are based on a conjectured limiting distribution, provided by Liu and Singh [J. Amer Statist. Assoc. 88 (1993) 252-260]. The present paper proves the conjecture under general regula...
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作者：Kim, Yongdai
作者单位：Seoul National University (SNU)
摘要：We study large sample properties of Bayesian analysis of the proportional hazard model with neutral to the right process priors on the baseline hazard function. We show that the posterior distribution of the baseline cumulative hazard function and regression coefficients centered at the maximum likelihood estimator is jointly asymptotically equivalent to the sampling distribution of the maximum likelihood estimator.
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作者：Coram, Marc; Lalley, Steven P.
作者单位：University of Chicago
摘要：do nonparametric Bayesian procedures overfit? To shed light on this question, we consider a binary regression problem in detail and establish frequentist consistency for a certain class of Bayes procedures based on hierarchical priors, called uniform mixture priors. These are defined as follows: let v be any probability distribution on the nonnegative integers. To sample a function f from the prior pi(v), first sample m from v and then sample f uniformly from the set of step functions from [0,...
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作者：Koltchinskii, Vladimir
作者单位：University System of Georgia; Georgia Institute of Technology; University of New Mexico
摘要：Let F be a class of measurable functions f : S -> [0, 1] defined on a probability space (S, A, P). Given a sample (X-1,X-...,X- X-n) of i.i.d. random variables taking values in S with common distribution P, let P-n denote the empirical measure based on (X-1,X-...,X- X-n). We study an empirical risk minimization problem P-n f -> min, f is an element of F. Given a solution (f) over cap (n) of this problem, the goal is to obtain very general upper bounds on its excess risk E-p((f) over cap (n)) ;...
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作者：Romano, Joseph P.; Shaikh, Azeem M.
作者单位：Stanford University; Stanford University
摘要：Consider the multiple testing problem of testing null hypotheses H-1,..., H-S. A classical approach to dealing with the multiplicity problem is to restrict attention to procedures that control the familywise error rate (FWER), the probability of even one false rejection. But if s is large, control of the FWER is so stringent that the ability of a procedure that controls the FWER to detect false null hypotheses is limited. It is therefore desirable to consider other measures of error control. T...
