Screening among Multivariate Normal Data

Abstract

This paper considers the problem of screening k multivariate normal populations (secondary data) with respect to a control population (primary data) in terms of covariance structure. A screening procedure, developed based upon statistical ranking and selection theory, is designed to include in the selected subset those populations which have the same (or similar) covariance structure as the control population, and exclude those populations which differ significantly. Formulas for computing the probability of a correct selection and the least favorable configuration are developed. The sample size required to achieve a specific probability requirement is also developed, with results presented in tabular form. This secondary data selection procedure is illustrated via an example with applications to radar signal processing. Academic PressAMS 1991 subject classifications: 62E15, 62F07, 62H10. Key words and phrases: hypergeometric function in matrix argument, indifference zone approach, eigenvalue, least favorable configuration, multivariate normal, probability of a correct screening, radar signal processing, ranking and selection, subset selection approach.

Robust adaptive signal processing methods for heterogeneous radar clutter scenarios

“…The rationale underlying our technique is that a peak in the RMB beamformer output occurs when training data is contaminated by l z i , is used in step 2 as opposed to the square root of the APR. A number of e orts [3][4][5]17,26,27,[34][35][36] have considered the use of the GIP for selecting representative training data while [8,16] use the GIP normalization for covariance estimation in compound Gaussian clutter. A comparison of the FML, SCRFML/APR, and SCRFML/GIP methods is shown using data from the RLSTAP hi-ÿdelity clutter model [24].…”

Statistical analysis of the non-homogeneity detector for STAP applications

“…In these scenarios, the test cell disturbance covariance matrix, RT, differs significantly from the estimated covariance matrix, R, formed using target-free disturbance realizations from adjacent reference cells. If a large number of test cell data realizations are available, the underlying non-homogeneity is characterized via the eigenvalues of R-1 RT [8]. However, in radar applications, only a single realization of test cell data is usually available.…”

Statistical Analysis of the Nonhomogeniety Detector for Stap Applications

“…It was shown in [12] that the distribution information of a class of multivariate probability density functions (PDF) is succinctly determined through an equivalent univariate PDF of a quadratic form. An application of this result is the non-homogeneity detector (NHD) based on the generalized inner product (GIP) [1][2][3][4]8,13].…”