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

• Activity Number: 251
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Yoshinori Kawasaki*+ and Akifumi Notsu and Shinto Eguchi
• Companies: Institute of Statistical Mathematics and Graduate University for Advanced Studies and Institute of Statistical Mathematics
• Keywords: Gaussian copula ; ??-estimator ; misspecification ; mixture distribution ; projective power entropy

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.