LINEAR METHODS IN STATISTICS

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The objective of this project is to study linear methods of statistics and their applications to biomedical research. Further results have been obtained for the problem of optimally estimating the variance components in an analysis of variance. These new methods are now shown to be ring-theoretic in nature as well as simple to calculate. This underlying algebraic nature of the solutions represents also a new body of technique in the statistical literature, and hence promises a new avenue of research in mathematical statistics generally. The collected material is presently being brought together in a book in preparation, and will provide a complete overview of the unbiased estimation of variance components as well as help mediate the introduction of algebraic structural methods into the statistical literature. Collaborative work was completed with Dr. G. Crabtree (NCI/DCBD/LP) on the evolution of the three fibrinogen genes. Several probabilistic models were constructed to deal with the problem of data, which by the nature of the problem is inaccessible to the researcher. Specifically, the pattern of present or absent introns on the genes was studied in an effort to determine the historical development of the genes, and one class of observations is that for which an intron is absent on all three genes, its presence thus being indetectable on the present day genes.