Accession Number : ADA283825


Title :   Eigenvalue Tests and Distributions for Small Sample Order Determination for Complex Wishart Matrices


Descriptive Note : Final rept. 1984-1994


Corporate Author : OFFICE OF NAVAL RESEARCH ARLINGTON VA


Personal Author(s) : Caldwell, Curtis I


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/a283825.pdf


Report Date : 13 Aug 1994


Pagination or Media Count : 939


Abstract : This thesis looks at tests to determine how many signal sources exist in the medium when constrained to using only a few samples. It applies classical hypothesis testing assuming complex multivariate Gaussian random variables. The critical issue is the derivation of probability density functions of appropriate test statistics. This thesis includes a comprehensive development of the tools of statistics of complex variables for engineers and physicists. This includes complex matrix derivatives, changes of complex variables, and properties of the characteristic function of a complex multivariate random variable. Probability density functions are derived for: the set of eigenvalues satisfying the generalized eigenvalue problem of two complex Wishart matrices, the matrix complex Normal distribution, a joint distribution needed to derive the density for the sphericity test statistic, ratio of averages of disjoint sums of sequential eigenvalues of a complex Wishart matrix, and several tests based on the ratio of an arbitrary eigenvalue. Mathematical statistics, Probability, Hypothesis tests, Complex variables, Principal components analysis, Complex Wishart distribution, Eigen-structure signal processing


Descriptors :   *WISHART MATRICES , SIGNAL PROCESSING , MAXIMUM LIKELIHOOD ESTIMATION , MULTIVARIATE ANALYSIS , STATISTICAL TESTS , RANDOM VARIABLES , WHITE NOISE , THESES , EIGENVALUES , PROBABILITY DENSITY FUNCTIONS , ACOUSTIC SIGNALS , ACOUSTIC EMISSIONS , NORMAL DISTRIBUTION , COMPLEX VARIABLES


Subject Categories : Numerical Mathematics
      Statistics and Probability
      Acoustics


Distribution Statement : APPROVED FOR PUBLIC RELEASE