Applications of Multivariate Analysis
Final rept. 1 May 1991-31 Jan 1993
PENNSYLVANIA STATE UNIV UNIVERSITY PARK CENTER FOR MULTIVARIATE ANALYSIS
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Research was carried out in a number of areas of multivariate analysis. New methods have been proposed in the theory of M-estimation to safeguard against outliers. Asymptotic distributions have been derived under a minimal set of assumptions. Bootstrap techniques are extended to nonstandard situations. Theoretical and computational aspects of bootstrap are reviewed. Exact tests have been developed to test the significance of parent-offspring correlations. New methods have been devised for multitarget tracking. The new methods are found to be satisfactory as they depend on minimal assumptions and involve simpler computational algorithms. In the area of probability, Edgeworth expansions have been extended to cover the cases where some of the variables are not continuous, which is considered as a major advance from the point of view of practical applications. A new differential geometric structure of a statistical model is proposed which is more general and more informative than those considered earlier. The methods are applied to study properties of estimates of parameters.
- Statistics and Probability