作者：Cholaquidis, Alejandro; Cuevas, Antonio; Fraiman, Ricardo
作者单位：Universidad de la Republica, Uruguay; Autonomous University of Madrid
摘要：A domain S subset of R-d is said to fulfill the Poincare cone property if any point in the boundary of S is the vertex of a (finite) cone which does not otherwise intersects the closure (S) over bar. For more than a century, this condition has played a relevant role in the theory of partial differential equations, as a shape assumption aimed to ensure the existence of a solution for the classical Dirichlet problem on S. In a completely different setting, this paper is devoted to analyze some s...
作者：Lepski, Oleg; Serdyukova, Nora
作者单位：Aix-Marseille Universite; Universidad de Concepcion
摘要：The problem of adaptive multivariate function estimation in the single-index regression model with random design and weak assumptions on the noise is investigated. A novel estimation procedure that adapts simultaneously to the unknown index vector and the smoothness of the link function by selecting from a family of specific kernel estimators is proposed. We establish a pointwise oracle inequality which, in its turn, is used to judge the quality of estimating the entire function (global oracle...
