Abstract #300101

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JSM 2003 Abstract #300101
Activity Number: 54
Type: Contributed
Date/Time: Sunday, August 3, 2003 : 4:00 PM to 5:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #300101
Title: Empirical Likelihood with Nonparametric Nuisance Functions
Author(s): Ingrid Van Keilegom*+ and Ian W. McKeague and Nils L. Hjort
Companies: Universite Catholique De Louvain and Florida State University and University of Oslo
Address: Institut De Statistique, 1348 Louvain-la-Neuve, , , Belgium
Keywords: empirical likelihood ; nonparametric regression ; plug-in
Abstract:

In this talk we develop the empirical likelihood (EL) theory for a finite dimensional parameter \theta_0, defined via an equation that depends on a nonparametric nuisance function h_0, i.e., E[m(Z,\theta,h_0)]=0 for \theta=\theta_0 for some function m depending on the random vector Z. We adopt the approach to replace the unknown function h_0 by a nonparametric estimator \hat h, and obtain general conditions under which -2 \log R_n(\theta_0,\hat h) (R_n(\theta_0,\hat h) being the nonparametric likelihood ratio function converges to a weighted sum of \chi^2_1 variables. The estimation of the weights is discussed. An extension to the EL theory for functions \theta_0(\cdot) (as opposed to parameters) is also given. Several examples are given, including the construction of confidence intervals/bands for functionals of survival distributions, for the error distribution in (non)parametric regression, and for the distribution function of current status data. This is joint work with Nils L. Hjort and Ian McKeague.

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