Tail Index Regression

Hansheng Wang Hansheng Wang is an Associate Professor of Statistics at Guanghua School of Management, Peking University, Beijing 100871, P. R. China . Chih-Ling Tsai is the Robert W. Glock Chair Professor in Management at Graduate School of Management, University of California, Davis, CA 95616-8609 . The authors are very grateful to the Editor, the AE, and one anonymous referee for constructive comments and valuable suggestions, which lead to a substantially improved manuscript. Wang’s research is supported in part by a NSFC grant (No. 10771006).

Chih-Ling Tsai Hansheng Wang is an Associate Professor of Statistics at Guanghua School of Management, Peking University, Beijing 100871, P. R. China . Chih-Ling Tsai is the Robert W. Glock Chair Professor in Management at Graduate School of Management, University of California, Davis, CA 95616-8609 . The authors are very grateful to the Editor, the AE, and one anonymous referee for constructive comments and valuable suggestions, which lead to a substantially improved manuscript. Wang’s research is supported in part by a NSFC grant (No. 10771006).

Abstract

In extreme value statistics, the tail index is an important measure to gauge the heavy-tailed behavior of a distribution. Under Pareto-type distributions, we employ the logarithmic function to link the tail index to the linear predictor induced by covariates, which constitutes the tail index regression model. We then propose an approximate log-likelihood function to obtain regression parameter estimators, and subsequently show the asymptotic normality of those estimators. Numerical studies are presented to illustrate theoretical findings.

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