JSM 2005 - Toronto

Abstract #304634

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 362
Type: Contributed
Date/Time: Wednesday, August 10, 2005 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract - #304634
Title: Developing Empirical Likelihood under Long-range Dependence
Author(s): Daniel J. Nordman*+ and Soumendra N. Lahiri
Companies: University of Wisconsin, La Crosse and Iowa State University
Address: 1725 State Street, La Crosse, WI, 54601, United States
Keywords: empirical likelihood ; estimating equations ; long-range dependence ; periodogram ; spectral distribution ; Whittle estimation
Abstract:

Our focus is the development of empirical likelihood (EL) methods for linear time series that exhibit long-range dependence or strong forms of dependence. For weakly or short-range dependent time processes, Kitamura (1997) proposed a version of EL (blockwise EL) based on data blocking techniques that have successfully lead to other nonparametric likelihoods, such as the block bootstrap. This talk explains why blockwise EL, like the block bootstrap Lahiri (1993), is difficult to extend to long-range dependent time processes. One problem is that blockwise EL ratios involve block adjustment factors to ensure limiting chi-square distributions, and these adjustments are natural to formulate under weak dependence but complicated under strong dependence. As an alternative to data blocking, we introduce a new version of empirical likelihood based on the periodogram (a data transformation) and spectral estimating equations. Under both weak dependence and strong forms of dependence, the method results in likelihood ratios that can be used to build nonparametric, asymptotically correct confidence regions for spectral parameters.

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Revised March 2005