This research concerns statistical inference for: (1) Lattice models for conditional independence in a multivariate normal distribution; (2) normal models with lattice restrictions on both the mean vector and covariance matrix; (3) non-nested missing data models; (4) group symmetry covariance models; (5) covariance models combining lattice conditional independence restrictions and group symmetry conditions; (6) characterizing transitive actions of generalized lower triangular matrix groups; (7) extensions of Hadamard's inequality for the determinant of a positive definite matrix; (8) consistency of invariant multivariant tests; (9) bounds for tail probabilities of weighted sums of independent gamma random variables; and (10) combining independent significance tests - a defense of Fisher's combination procedure. This research is in the general area of statistics and probability. The problems are attacked by a combination of algebraic and analytic techniques, including the theory of group representations, distributive lattice theory, and invariant (Haar) measures, in order to characterize the structure of the models and to determine distributional and decision-theoretic properties of estimators and test characteristics.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Application #
8902211
Program Officer
Alan Izenman
Project Start
Project End
Budget Start
1989-06-01
Budget End
1993-05-31
Support Year
Fiscal Year
1989
Total Cost
$239,640
Indirect Cost
Name
University of Washington
Department
Type
DUNS #
City
Seattle
State
WA
Country
United States
Zip Code
98195