On Total-Variance Reduction Via Thresholding-Based Spectral Analysis

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 prior 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, the other on a Bayesian information criterion selection rule. As an example application we consider cepstral analysis and we show via numerical simulation that the simple thresholding scheme proposed herein can achieve significant reductions of total variance