Kernel smoothing of periodograms under Kullback-Leibler discrepancy

Authors:
Jan Hannig;Thomas C. M. Lee
Affiliations:
Department of Statistics, Colorado State University, Fort Collins, CO;Department of Statistics, Colorado State University, Fort Collins, CO
Venue:
Signal Processing
Year:
2004

Citing 5
Cited 1

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A stabilized bandwidth selection method for kernel smoothing of the periodogram

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Abstract

Kernel smoothing on the periodogram is a popular nonparametric method for spectral density estimation. Most important in the implementation of this method is the choice of the bandwidth, or span, for smoothing. One idealized way of choosing the bandwidth is to choose it as the one that minimizes the Kullback-Leibler (KL) discrepancy between the smoothed estimate and the true spectrum. However, this method fails in practice, as the KL discrepancy is an unknown quantity. This paper introduces an estimator for this discrepancy, so that the bandwidth that minimizes the unknown discrepancy can be empirically approximated via the minimization of it. It is shown that this discrepancy estimator is consistent. Numerical results also suggest that this empirical choice of bandwidth often outperforms some other commonly used bandwidth choices. The same idea is also applied to choose the bandwidth for log-periodogram smoothing.