Showing papers on "Covariance mapping published in 1969"

On the Exact Covariance of Products of Random Variables

Abstract: For the general case of jointly distributed random variables x and y, Goodman [3] derives the exact variance of the product xy. For the special case where x and y are stochastically independent, he provides a simpler expression for the exact variance. We offer a weaker set of assumptions which suffices to yield the simpler expression. We then extend Goodman's analysis to present the exact covariance of two products xy and uv, and sketch several specializations and applications.

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)

On the extraction of pattern features from continuous measurements

Abstract: A suboptimum method of extracting features, by linear operations, from continuous data belonging to M pattern classes is presented. The set of features selected minimizes bounds on the probability of error obtained from the Bhattacharyya distance and the Hajek divergence. The random processes associated with the pattern classes are assumed to be Gaussian with different means and covariance functions. For M=2, in the two special cases in which, respectively, the means and the covariance functions are the same, both the above distance measures yield the same answer. The results obtained represent an extension of the existing results for two pattern classes with the same means and different covariance functions.

Applied spectral analysis of mixed random and deterministic processes.

Abstract: : Contents: Spectral analysis of nonstationary random processes; Numerical estimates for averages, variances, and standard deviations; Numerical estimates for the covariance and covariance spectrum; Smoothing, continuous and discrete; Spectral analysis of a single sample function; Calculation of the covariance spectrum for a nonstationary process.