JSM 2004 - Toronto

Abstract #301839

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Activity Number: 118
Type: Contributed
Date/Time: Monday, August 9, 2004 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract - #301839
Title: Localized Kullback-Leibler Method for Spectral Estimation
Author(s): Jianzhong Liu*+ and Hernando Ombao
Companies: University of Illinois and University of Illinois
Address: Dept. of Statistics, Champaign, IL, 61820,
Keywords: bandwidth selection ; localized Kullback-Leibler distance ; periodograms ; spectrum ; generalized additive models
Abstract:

A consistent estimator for the spectral density of a stationary random process can be obtained by smoothing the periodograms across frequency. The degree of smoothness of many spectra may change over frequency. Thus, it is reasonable to choose a span that also varies across frequency. We will propose a variable span selection method that is based on the Kullback-Leibler distance between the raw and smoothed periodograms. Our approach is to form a localized neighborhood around each frequency; compute the Kullback-Leibler distance and finally select a frequency-specific optimal bandwidth. This criterion, originally developed for use in fitting generalized additive models, utilizes the approximate full local likelihood of periodograms, which asymptotically behave like independently distributed gamma random variables. The resulting span selector is simple and easy to implement. We will present simulation results and analysis of time series dataset.

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