## Asymptotically Robust Tests about Covariance Matrices |

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### Contents

Nonrobustness of Normaltheory Procedures | 15 |

Largesample Tests for Equality of Covariance | 27 |

k Asymptotic Comparisons of the Tests for Equality | 49 |

1 other sections not shown

### Common terms and phrases

approximate Pitman relative asymptotic distribution asymptotic normality asymptotic variance asymptotically robust Bahadur efficiency bivariate distribution bivariate populations Box test Box to standard canonical correlations common kurtosis computed convergence Doctor of Philosophy elementary symmetric functions equality of covariance evaluated f(Xn finite fourth moments Gleser Gnanadesikan's test identically distributed independently and identically large-sample tests likelihood-ratio test log t2Q log tQ2 Math matrix of real measure of asymptotic multivariate normal distribution n-hn non-normal non-robustness normal-theory procedures normal-theory tests null hypothesis p-variate Pitman efficiency Pitman relative efficiency positive numbers procedures for testing Proof random matrices random vectors real elements roots of ST Roy and Gnanadesikan's second partials second-order moments second-order sample moments sequence of alternatives sequence of random sequences of test standard error test symmetric matrix tanh tanh(tanh test based test for equality test statistics testing H theorem 1.8 transformation