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Abstract:
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In multivariate analysis, the assumption of equality of covariances is often made. In some applications, the equality of covariance is tested after the fact from residuals assuming multivariate normal distribution. In this talk, we present new nonparametric methods for testing homogeneity of covariance matrices. The methods rely on a recent multivariate theory developed for a large number of factor levels. First, the extension of these results to cover the situation where both sample size and factor levels tend to infinity is discussed. The results are then applied to construct a test whether the covariance matrix depends on one or more of the predictors. Other possible applications of the results included lack of fit tests and nonparametric multivariate analysis of covariance will also be discussed. Simulation results will be presented to show the performance of the tests under various practical scenarios. The methods will be illustrated with data from a smoking cessation trial.
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