Smoothing an indefinite variance-covariance matrix

Abstract

The usual estimator of the dispersion matrix has a distinct advantage over other estimation procedures since it is computationally feasible for a data set with a substantial number of missing observations. However, this estimator, when the data vectors have some missing elements, may not have the required property of being at least positive semidefinite. The smoothing procedure suggested in this paper rectifies this deficiency. In addition, com-putational procedures are proposed. The smoothing procedure is illustrated by an example and a Monte Carlo experiment shows that smoothing substantially increases the power of the test proposed by Kleinbaum(1973).