Abstract
Abstract : The usual assumption in multivariate hypothesis testing is that the sample consists of n independent, identically distributed Gaussian p-vectors. In this dissertation this assumption is weakened by considering a class of distributions for which the vector observation are not necessarily Gaussian or independent. The following hypothesis testing problems are considered: testing for equality between the mean vector and a specified vector, lack of correlations among different sets, equality of covariance matrices and mean vectors, equality between the correlation coefficient and a specified number, and MANOVA. For each of the above hypotheses, invariant tests and their properties are developed. These include the uniformly most powerful test, the locally most powerful test, admissibility, and null and non-null distributions. Keywords include: Invariant test; likelihood ratio test; multivariate elliptically contoured distribution; admissibility locally most powerful invariant test; maximal invariant; maximum likelihood estimation.
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