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Abstract:
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This paper investigates the impact on various multivariate statistical entities including Hotelling's T-square, the Mahalanobis distance function, etc. due to the erroneous inclusion or erroneous exclusion of variables. For example, this impact will occur in multivariate testing hypotheses on the population multivariate mean vector and in constructing confidence ellipsoids for the p-dimensional mean under multivariate normality. Suppose X is a k by 1 vector and suppose p-k additional variables (p>k) are added to X, then the question is how the Hotelling's T-square and other multivariate statistics change? The new entity is to be detailed and simplified to a function of the original entity. Initially, the one-sample and two-sample multivariate statistical entities (e.g. such as Hotelling's T-square) will be examined in this study followed by a generalization to the multivariate case.
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