The Rao test for testing handedness of complex-valued covariance matrix

Abstract

Banding the inverse of covariance matrix has become a popular technique to estimate a high dimensional covariance matrix from limited number of samples. However, little work has been done in providing a criterion to determine when a matrix is bandable. In this paper, we present a detector to test the bandedness of a Cholesky factor matrix. The test statistic is formed based on the Rao test, which does not require the maximum likelihood estimates under the alternative hypothesis. In many fields, such as radar signal processing, the covariance matrix and its unknown parameters are often complex-valued. We focus on dealing with complex-valued cases by utilizing the complex parameter Rao test, instead of the traditional real Rao test. This leads to a more intuitive and efficient test statistic. Examples and computer simulations are given to investigate the derived detector performance.