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Invariance Properties Of Statistical Tests For Dependent Observations, Akhil K. Vaish

Mathematics & Statistics Theses & Dissertations

In this dissertation we assume that the observations are from normal populations but are correlated and study the problem of characterizing the class of covariance structures such that the distributions of the popular test statistics remain invariant, that is, they remain the same except for a constant factor. We first obtain some simple extensions and variations of the well known Cauchy-Schwarz inequality. Incidentally, several inequalities that are useful in the detection of outliers can be deduced from our results.

Our main result is a characterization of the class of all nonnegative definite solutions W to the matrix equation AWA = …