Screening among Multivariate Normal Data

This paper considers the problem of screeningkmultivariate 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.

[1]  Calyampudi R. Rao,et al.  Linear Statistical Inference and Its Applications. , 1975 .

[2]  E. J. Kelly.  An Adaptive Detection Algorithm , 1986, IEEE Transactions on Aerospace and Electronic Systems.

[3]  W. R. Buckland,et al.  Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability. , 1952 .

[4]  Calyampudi Radhakrishna Rao,et al.  Linear Statistical Inference and its Applications , 1967 .

[5]  Jaime R. Roman,et al.  Multichannel System Identification and Detection Using Output Data Techniques , 1993 .

[6]  H. Hotelling.  A Generalized T Test and Measure of Multivariate Dispersion , 1951 .

[7]  Calyampudi R. Rao,et al.  Test for a specified signal when the noise convariance matrix is unknown , 1987 .

[8]  R. Bechhofer.  A Single-Sample Multiple Decision Procedure for Ranking Means of Normal Populations with known Variances , 1954 .

[9]  D L Streiner,et al.  An Introduction to Multivariate Statistics , 1993, Canadian journal of psychiatry. Revue canadienne de psychiatrie.

[10]  S. Gupta,et al.  SOME SELECTION AND RANKING PROCEDURES FOR MULTIVARIATE NORMAL POPULATIONS. , 1968 .

[11]  David J. McLaughlin,et al.  CFAR detection in clutter with unknown correlation properties , 1995 .

[12]  C. G. Khatri,et al.  Some Distribution Problems Connected with the Characteristic Roots of $S_1S^{-1}_2$ , 1967 .

[13]  T. W. Anderson.  An Introduction to Multivariate Statistical Analysis , 1959 .

[14]  A. James.  Distributions of Matrix Variates and Latent Roots Derived from Normal Samples , 1964 .