Total-Variance Reduction Via Thresholding: Application to Cepstral Analysis

We consider a vector of independent normal random variables with unknown means but known variances. Our problem is to reduce the total variance of these random variables by exploiting the a priori information that a significant proportion of them have "small" means. We show that thresholding is an effective means of solving this problem and propose two schemes for threshold selection: one based on a uniformly most powerful unbiased test and another on a Bayesian information criterion selection rule. Reduction of the total variance of estimated spectra, obtained by cepstral analysis, can be cast in the above mathematical framework, and we use it as an example application throughout this paper. We show via numerical simulation that the use of the simple thresholding method, proposed here, in cepstral analysis can achieve significant reductions of total variance