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作者：Peng, Liang; Qi, Yongcheng
作者单位：University System of Georgia; Georgia Institute of Technology; University of Minnesota System; University of Minnesota Duluth
摘要：Estimating high quantiles plays an important role in the context of risk management. This involves extrapolation of an unknown distribution function. In this paper we propose three methods, namely, the normal approximation method, the likelihood ratio method and the data tilting method, to construct confidence regions for high quantiles of a heavy tailed distribution. A simulation study prefers the data tilting method.
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作者：Clarke, B.; Yuan, Ao
作者单位：University of British Columbia; Howard University
摘要：Sample size criteria are often expressed in terms of the concentration of the posterior density, as controlled by some sort of error bound. Since this is done pre-experimentally, one can regard the posterior density as a function of the data. Thus, when a sample size criterion is formalized in terms of a functional of the posterior, its value is a random variable. Generally, such functionals have means under the true distribution. We give asymptotic expressions for the expected value, under a ...
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作者：Kleun, B. J. K.; Van der Wart, A. W.
作者单位：Vrije Universiteit Amsterdam
摘要：We consider the asymptotic behavior of posterior distributions if the model is misspecified. Given a prior distribution and a random sample from a distribution P-0, which may not be in the support of the prior, we show that the posterior concentrates its mass near the points in the support of the prior that minimize the Kullback-Leibler divergence with respect to P0. An entropy condition and a prior-mass condition determine the rate of convergence. The method is applied to several examples, wi...
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作者：Pensky, Marianna
作者单位：State University System of Florida; University of Central Florida
摘要：The present paper investigates theoretical performance of various Bayesian wavelet shrinkage rules in a nonparametric regression model with i.i.d. errors which are not necessarily normally distributed. The main purpose is comparison of various Bayesian models in terms of their frequentist asymptotic optimality in Sobolev and Besov spaces. We establish a relationship between hyperparameters, verify that the majority of Bayesian models studied so far achieve theoretical optimality, state which B...
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作者：Senturk, Damla; Muller, Hans-Georg
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; University of California System; University of California Davis
摘要：We consider covariate adjusted regression (CAR), a regression method for situations where predictors and response are observed after being distorted by a multiplicative factor. The distorting factors are unknown functions of an observable covariate, where one specific distorting function is associated with each predictor or response. The dependence of both response and predictors on the same confounding covariate may alter the underlying regression relation between undistorted but unobserved p...
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作者：Robins, James; Van der Vaart, Aad
作者单位：Harvard University; Harvard T.H. Chan School of Public Health; Vrije Universiteit Amsterdam
摘要：We construct honest confidence regions for a Hilbert space-valued parameter in various statistical models. The confidence sets can be centered at arbitrary adaptive estimators, and have diameter which adapts optimally to a given selection of models. The latter adaptation is necessarily limited in scope. We review the notion of adaptive confidence regions, and relate the optimal rates of the diameter of adaptive confidence regions to the minimax rates for testing and estimation. Applications in...
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作者：Chen, Willa W.; Hurvich, Clifford M.
作者单位：Texas A&M University System; Texas A&M University College Station; New York University
摘要：We consider a common-components model for multivariate fractional cointegration, in which the s >= 1 components have different memory parameters. The cointegrating rank may exceed 1. We decompose the true cointegrating vectors into orthogonal fractional cointegrating subspaces such that vectors from distinct subspaces yield cointegrating errors with distinct memory parameters. We estimate each cointegrating subspace separately, using appropriate sets of eigenvectors of an averaged periodogram ...
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作者：Wei, Ying; He, Xuming
作者单位：Columbia University; University of Illinois System; University of Illinois Urbana-Champaign
摘要：Growth charts are often more informative when they are customized per subject, taking into account prior measurements and possibly other covariates of the subject. We study a global semiparametric quantile regression model that has the ability to estimate conditional quantiles without the usual distributional assumptions. The model can be estimated from longitudinal reference data with irregular measurement times and with some level of robustness against outliers, and it is also flexible for i...
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作者：Hall, Peter; Maiti, Tapabrata
作者单位：Australian National University; Iowa State University
摘要：Nested-error regression models are widely used for analyzing clustered data. For example, they are often applied to two-stage sample surveys, and in biology and econometrics. Prediction is usually the main goal of such analyses, and mean-squared prediction error is the main way in which prediction performance is measured. In this paper we suggest a new approach to estimating mean-squared prediction error. We introduce a matched-moment, double-bootstrap algorithm, enabling the notorious underes...
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作者：Levina, Elizaveta; Bickel, Peter J.
作者单位：University of Michigan System; University of Michigan; University of California System; University of California Berkeley
摘要：This paper introduces a nonparametric algorithm for bootstrapping a stationary random field and proves certain consistency properties of the algorithm for the case of mixing random fields. The motivation for this paper comes from relating a heuristic texture synthesis algorithm popular in computer vision to general nonparametric bootstrapping of stationary random fields. We give a formal resampling scheme for the heuristic texture algorithm and prove that it produces a consistent estimate of t...
