An information-theoretic framework for robustness |
| |
Authors: | Stephan Morgenthaler Clifford Hurvich |
| |
Institution: | (1) EPFL-DMA, Swiss Federal Institute of Technology, 1015 Lausanne, Switzerland;(2) New York University, 735 Tisch Hall, Washington Sq., 10003 New York, NY, U.S.A. |
| |
Abstract: | This is a paper about the foundation of robust inference. As a specific example, we consider semiparametric location models that involve a shape parameter. We argue that robust methods result via the selection of a representative shape from a set of allowable shapes. To perform this selection, we need a measure of disparity between the true shape and the shape to be used in the inference. Given such a disparity, we propose to solve a certain minimax problem. The paper discusses in detail the use of the Kullback-Leibler divergence for the selection of shapes. The resulting estimators are shown to have redescending influence functions when the set of allowable shapes contains heavy-tailed members. The paper closes with a brief discussion of the next logical step, namely the representation of a set of shapes by a pair of selected shapes. |
| |
Keywords: | Robustness distributional shapes Kullback-Leibler divergence |
本文献已被 SpringerLink 等数据库收录! |
|