An Interpretation of Choi's KL Spectrum

다국어 초록 (Multilingual Abstract)

Choi(1990) has presented the KL spectrum that minimizes the frequency-domain Kull-gack-Leibler information number. Alos, a method of modifying a spectrum estimate has been suggested, which is based of the KL spectrum. Some numerical examples have illustrated that the KL spectrum estimate is superior to the initial estimate, i.e., the autocovariances obtained by the inversed Fourier transformation of the KL spectrum estimate are closer to the sample autocovariances of the given observations than those of the initial spectrum estimate. Choi(1991) shows that a Gaussian AR(P) process is the closest in the timne-domain Kullback-Leibler sense to independently and identically distributed normal random variables subject to the first p+1 autocovariance constrainst. It gives a rationale to the existence of the KL spectrum. One of the purpose of this paper is to present additional motivation for using the KL spectrum. One of the purpose of this paper is to present additional motivation for using the KL measure to select an optimal spectrum and another is to persent a detailed proof of the latter theorem.