-
作者：Beran, R
作者单位：University of California System; University of California Berkeley
-
作者：Fraiman, R; Yohai, VJ; Zamar, RH
作者单位：Universidad de San Andres Argentina; University of Buenos Aires; Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET); University of British Columbia
摘要：We find optimal robust estimates for the location parameter of n independent measurements from a common distribution F that belongs to a contamination neighborhood of a normal distribution. We follow an asymptotic minimax approach similar to Huber's but work with full neighborhoods of the central parametric model including nonsymmetric distributions. Our optimal estimates minimize monotone functions of the estimate's asymptotic variance and bias, which include asymptotic approximations for the...
-
作者：Dümbgen, L
作者单位：University of Lubeck
-
作者：Taupin, ML
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：In the nonlinear structural errors-in-variables model, we propose a consistent estimator of the unknown parameter using a modified least squares criterion. We give an upper bound of its rate of convergence which is strongly related to the regularity of the regression function and is generally slower than the parametric rate of convergence n(-1/2). Nevertheless, the rate is of order n-(1/2) for some particular analytic regression functions. For instance, when the regression Function is either a...
-
作者：Drees, H
作者单位：Ruprecht Karls University Heidelberg
摘要：Asymptotic minimax risk bounds for estimators of a positive extreme value index under zero-one loss are investigated in the classical i.i.d. setup. To this end, we prove the weak convergence of suitable local experiments with Pareto distributions as center of localization to a white noise model, which was previously studied in the context of nonparametric local density estimation and regression. From this result we derive upper and lower bounds on the asymptotic minimax risk in the local and i...
-
作者：Berrendero, JR; Zamar, RH
作者单位：Autonomous University of Madrid; University of British Columbia
摘要：Maximum bias curves for some regression estimates were previously derived assuming that (i) the intercept term is known and/or (ii) the regressors have an elliptical distribution. We present a single method to obtain the maximum bias curves for a large class of regression estimates. Our results are derived under very mild conditions and, in particular, do not require the restrictive assumptions (i) and (ii) above. Using these results it is shown that the maximum bias curves heavily depend on t...
-
作者：Hartigan, JA
作者单位：Yale University
-
作者：Davies, PL; Kovac, A
作者单位：University of Duisburg Essen
-
作者：Marron, JS
作者单位：University of North Carolina; University of North Carolina Chapel Hill
-
作者：Fan, JQ; Zhang, CM; Zhang, J
作者单位：Chinese University of Hong Kong; University of Wisconsin System; University of Wisconsin Madison; University of California System; University of California Los Angeles
摘要：Likelihood ratio theory has had tremendous success in parametric inference, due to the fundamental theory of Wilks. Yet, there is no general applicable approach for nonparametric inferences based on function estimation. Maximum likelihood ratio test statistics in general may not exist in nonparametric function estimation setting. Even if they exist, they are hard to find and can not; be optimal as shown in this paper. We introduce the generalized likelihood statistics to overcome the drawbacks...
