Affine Invariant Divergence with Empirical Estimability

• Activity Number: 36
• Type: Contributed
• Date/Time: Sunday, August 4, 2013 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Hironori Fujisawa*+ and Takafumi Kanamori
• Companies: The Institute of Statistical Mathematics and Nagoya University
• Keywords: Affince Invariance ; Cross Entropy ; Divergence ; Empirically Estimable ; Regression ; Robustness

Abstract

In statistical inference, divergences play an important role. Divergences are regarded as an extension of squared distances defined over a set of probability distributions. An estimator of parameter can be obtained as the minimizer of divergence. In this paper, we study statistical properties of divergences in order to obtain robust minimum divergence estimators. In particular, we focus on an invariant divergence under affine transformation of data, and then we obtain an explicit class of divergences. Since affine transformations are often used for prepossessing of data analysis, the invariance is an important feature for estimators. For the specified class of divergences, we study a robustness property by applying a sensitivity analysis. We show some numerical experiments, and confirm the validity of the sensitivity analysis as a tool to understand statistical properties of minimum divergence estimators.