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作者：Shen, Xiaotong; Wang, Lifeng
作者单位：University of Minnesota System; University of Minnesota Twin Cities
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作者：Cai, TT; Low, MG
作者单位：University of Pennsylvania
摘要：Adaptive confidence balls are constructed for individual resolution levels as well as the entire mean vector in a multiresolution framework. Finite sample lower bounds are given for the minimum expected squared radius for confidence balls with a prespecified confidence level. The confidence balls are centered on adaptive estimators based on special local block thresholding rules. The radius is derived from an analysis of the loss of this adaptive estimator. In addition adaptive honest confiden...
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作者：Meinshausen, Nicolai; Rice, John
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of California System; University of California Berkeley
摘要：We consider the problem of estimating the number of false null hypotheses among a very large number of independently tested hypotheses, focusing on the situation in which the proportion of false null hypotheses is very small. We propose a family of methods for establishing lower 100(l - alpha)% confidence bounds for this proportion, based on the empirical distribution of the p-values of the tests. Methods in this family are then compared in terms of ability to consistently estimate the proport...
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作者：Massart, Pascal; Nedelec, Elodie
作者单位：Universite Paris Saclay
摘要：We propose a general theorem providing upper bounds for the risk of an empirical risk minimizer (ERM). We essentially focus on the binary classification framework. We extend Tsybakov's analysis of the risk of an ERM under margin type conditions by using concentration inequalities for conveniently weighted empirical processes. This allows us to deal with ways of measuring the size of a class of classifiers other than entropy with bracketing as in Tsybakov's work. In particular, we derive new ri...
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作者：Bischoff, Wolfgang; Miller, Frank
作者单位：AstraZeneca
摘要：Linear regression models are among the models most used in practice, although the practitioners are often not sure whether their assumed linear regression model is at least approximately true. In such situations, only designs for which the linear model can be checked are accepted in practice. For important linear regression models such as polynomial regression, optimal designs do not have this property. To get practically attractive designs, we suggest the following strategy. One part of the d...
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作者：Fuh, Cheng-Der
作者单位：Academia Sinica - Taiwan
摘要：Motivated by studying asymptotic properties of the maximum likelihood estimator (MLE) in stochastic volatility (SV) models, in this paper we investigate likelihood estimation in state space models. We first prove, under some regularity conditions, there is a consistent sequence of roots of the likelihood equation that is asymptotically normal with the inverse of the Fisher information as its variance. With an extra assumption that the likelihood equation has a unique root for each n, then ther...
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作者：Csiszár, I; Talata, Z
作者单位：Hungarian Academy of Sciences; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics
摘要：For Markov random fields on Z(d) with finite state space, we address the statistical estimation of the basic neighborhood, the smallest region that determines the conditional distribution at a site on the condition that the values at all other sites are given. A modification of the Bayesian Information Criterion, replacing likelihood by pseudo-likelihood, is proved to provide strongly consistent estimation from observing a realization of the field on increasing finite regions: the estimated ba...
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作者：James, Lancelot F.
作者单位：Hong Kong University of Science & Technology
摘要：Neutral to the right (NTR) processes were introduced by Doksum in 1974 as Bayesian priors on the class of distributions on the real line. Since that time there have been numerous applications to models that arise in survival analysis subject to possible right censoring. However, unlike the Dirichlet process, the larger class of NTR processes has not been used in a wider range of more complex statistical applications. Here, to circumvent some of these limitations, we describe a natural extensio...
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作者：Mueller, Ursula U.; Schick, Anton; Wefelmeyer, Wolfgang
作者单位：Texas A&M University System; Texas A&M University College Station; State University of New York (SUNY) System; Binghamton University, SUNY; University of Cologne
摘要：Conditional expectations given past observations in stationary time series are usually estimated directly by kernel estimators, or by plugging in kernel estimators for transition densities. We show that, for linear and nonlinear autoregressive models driven by independent innovations, appropriate smoothed and weighted von Mises statistics of residuals estimate conditional expectations at better parametric rates and are asymptotically efficient. The proof is based on a uniform stochastic expans...
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作者：Diaconis, Persi; Rolles, Silke W. W.
作者单位：Stanford University; Eindhoven University of Technology
摘要：We introduce a natural conjugate prior for the transition matrix of a reversible Markov chain. This allows estimation and testing. The prior arises from random walk with reinforcement in the same way the Dirichlet prior arises from Polya's urn. We give closed form normalizing constants, a simple method of simulation from the posterior and a characterization along the lines of W. E. Johnson's characterization of the Dirichlet prior.
