-
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...
-
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...
-
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...
-
作者：Fromont, Magalie; Laurent, Beatrice
作者单位：Universite Rennes 2; Universite de Rennes; Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National des Sciences Appliquees de Toulouse
摘要：Given an i.i.d. sample drawn from a density f, we propose to test that f equals some prescribed density fo or that f belongs to some translation/scale family. We introduce a multiple testing procedure based on an estimation of the L-2-distance between f and fo or between f and the parametric family that we consider. For each sample size n, our test has level of significance a. In the case of simple hypotheses, we prove that our test is adaptive: it achieves the optimal rates of testing establi...
-
作者：Bickel, Peter J.; Ritov, Ya'acov; Stoker, Thomas M.
作者单位：University of California System; University of California Berkeley; Hebrew University of Jerusalem; Massachusetts Institute of Technology (MIT)
摘要：We introduce a new framework for constructing tests of general semiparametric hypotheses which have nontrivial power on the n(-1/2) scale in every direction, and can be tailored to put substantial power on alternatives of importance. The approach is based on combining test statistics based on stochastic processes of score statistics with bootstrap critical values.
-
作者：Ho, Man-Wai
作者单位：National University of Singapore
摘要：A class of random hazard rates, which is defined as a mixture of an indicator kernel convolved with a completely random measure, is of interest. We provide an explicit characterization of the posterior distribution of this mixture hazard rate model via a finite mixture of S-paths. A closed and tractable Bayes estimator for the hazard rate is derived to be a finite sum over S-paths. The path characterization or the estimator is proved to be a Rao-Blackwellization of an existing partition charac...
-
作者：Komaki, Fumiyasu
作者单位：University of Tokyo
摘要：We investigate shrinkage priors for constructing Bayesian predictive distributions. It is shown that there exist shrinkage predictive distributions asymptotically dominating Bayesian predictive distributions based on the Jeffreys prior or other vague priors if the model manifold satisfies some differential geometric conditions. Kullback-Leibler divergence from the true distribution to a predictive distribution is adopted as a loss function. Conformal transformations of model manifolds correspo...
-
作者：Kulikov, Vladimir N.; Lopuhaa, Hendrik P.
作者单位：Delft University of Technology
摘要：We investigate the behavior of the nonparametric maximum likelihood estimator (f) over cap (n), for a decreasing density f near the boundaries of the support of f. We establish the limiting distribution of (f) over capn(n(-alpha)), where we need to distinguish between different values of 0 < alpha < 1. Similar results are obtained for the upper endpoint of the support, in the case it is finite. This yields consistent estimators for the values of f at the boundaries of the support. The limit di...
-
作者：Inoue, Akihiko; Kasahara, Yukio
作者单位：Hokkaido University
摘要：We consider the finite-past predictor coefficients of stationary time series, and establish an explicit representation for them, in terms of the MA and AR coefficients. The proof is based on the alternate applications of projection operators associated with the infinite past and the infinite future. Applying the result to long memory processes, we give the rate of convergence of the finite predictor coefficients and prove an inequality of Baxter-type.
-
作者：Dahlhaus, Rainer
作者单位：Ruprecht Karls University Heidelberg
