Table of Contents
ISRN Probability and Statistics
Volume 2013 (2013), Article ID 787141, 10 pages
http://dx.doi.org/10.1155/2013/787141
Research Article

Detection of Heterogeneous Structures on the Gaussian Copula Model Using Projective Power Entropy

1Department of Statistical Science, The Graduate University for Advanced Studies, Tachikawa, Tokyo 190-8562, Japan
2The Institute of Statistical Mathematics and The Graduate University for Advanced Studies, Tachikawa, Tokyo 190-8562, Japan

Received 22 July 2013; Accepted 19 September 2013

Academic Editors: E. Miranda and O. Pons

Copyright © 2013 Akifumi Notsu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We discuss a parameter estimation problem for a Gaussian copula model under misspecification. Conventional estimators such as the maximum likelihood estimator (MLE) do not work well if the model is misspecified. We propose the estimator that minimizes the projective power entropy. We call it the -estimator, where denotes the power index. A feasible form of the projective power entropy is given that suites the Gaussian copula model. It is shown that the -estimator is robust against outliers. In addition the -estimator can appropriately detect a heterogeneous structure of the underlying distribution, even if the underlying distribution consists of some different copula components while a single Gaussian copula is used as a statistical model. We explore such an ability of the -estimator to detect the local structures in the comparison with the MLE. We also propose a fixed point algorithm to obtain the -estimator. The usefulness of the proposed methodology is demonstrated in numerical experiments.