Fixed-B Asymptotics for Blockwise Empirical Likelihood

• Activity Number: 626
• Type: Invited
• Date/Time: Thursday, August 7, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Xianyang Zhang*+ and Xiaofeng Shao
• Companies: University of Missouri-Columbia and University of Illinois at Urbana-Champaign
• Keywords: Blocking ; Empirical likelihood ; Fixed-b asymptotics ; Time series

Abstract

In this paper, we describe an extension of the fixed-b approach introduced by Kiefer and Vogelsang (2005) to the empirical likelihood estimation framework. Under the fixed-b asymptotics, the empirical log-likelihood ratio statistic evaluated at the true parameter converges to a nonstandard yet pivotal limiting distribution which can be approximated numerically. The impact of the bandwidth parameter and kernel choice is reflected in the fixed-b limiting distribution. Compared to the Chi-squared based inference procedure used by Kitamura (1997) and Smith (2011), the fixed-b approach provides a better approximation to the finite sample distribution of the empirical log-likelihood ratio statistic; Correspondingly, as shown in our simulation studies, the confidence region based on the fixed-b approach has more accurate coverage than the traditional counterpart. If time permits, the upper bounds on the coverage probabilities of the blockwise empirical likelihood ratio confidence region will be discussed.