Multiwindow estimators of correlation

Abstract

This paper is concerned with the structure of estimators of correlation matrices and correlation sequences. We argue that reasonable estimators of the correlation matrix are quadratic in the data and nonnegative definite. We also specify the structure of the estimator when the data are modulated: a property we call modulation covariance. We state a representation theorem for estimators that have these attributes. We also derive a representation for estimators that have the additional requirement that the estimated matrix be Toeplitz. These representation theorems admit estimators that use multiwindowed copies of the data. In many circumstances, this multiwindow structure is superior to the conventional sum of lagged-products or outer-product estimators.