Testing and Estimation for a Circular Stationary Model

Abstract : Tests are conducted for x, a random vector having a p-variate normal distribution with a mean vector and specifically defined covariance matrix. On the basis of N independent observations on x, likelihood ratio tests of various hypotheses are considered. Tests are made (1) for symmetries in the covariance structure and (2) for means given that the covariance matrix is circular; (3) other tests enable means and covariances to be investigated simultaneously. Large sample results are obtained for both the central and noncentral cases. The structure of symmetry and circularity offers a more general model than that of the intra-class correlation or sphericity models previously considered. (Author)