Empirical Likelihood Confidence Band for Functional Parameter

• Activity Number: 484
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Saswata Sahoo*+ and Soumendra N. Lahiri
• Companies: North Carolina State University and North Carolina State University
• Keywords: Empirical likelihood ; estimating equations ; Wilk's theorem ; high dimension ; functional parameter ; confidence band

Abstract

Empirical likelihood confidence region, originally developed by Owen(1990) has been found to be particularly useful in high dimensional setup, where the data dimension and sample size both grow simultaneously, as stud- ied by Hjort et al(2009). In this paper, simultaneous confidence bands for functional parameter of the distribution by the empirical likelihood method are proposed and studied. In a nutshell, the proposed methods rely on the asymptotic distribution of the empirical log likelihood ratio under unbounded number of constraints, the constraints come into the setup in the form of estimating equations giving information on the functional parameter of interest. The methods include empirical likelihood under unbounded number of constraints without penalization and empirical likelihood with penalization. The limit distribution of the empirical likelihood ratio with and without penalization are derived. The proposed methods compare favorably with the empirical likelihood confidence band derived for quantiles by Einmahl, McKeague(1999). Finite sample properties of the proposed methods are studied by simulation under various situations.