Expected and unexpected values of individual Mahalanobis distances |
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Authors: | D. Dai P. Karlsson |
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Affiliation: | Department of Economics and Statistics, Linnaeus University, V?xj?, Sweden |
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Abstract: | This paper derives first-order sampling moments of individual Mahalanobis distances (MDs) in cases when the dimension p of the variable is proportional to the sample size n. Asymptotic expected values when n, p → ∞ are derived under the assumption p/n → c,?0 ? c < 1. It is shown that some types of standard estimators remain unbiased in this case, while others are asymptotically biased, a property that appears to be unnoticed in the literature. Second-order moments are also supplied to give some additional insight to the matter. |
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Keywords: | Expected values increasing dimension inverse covariance matrix mahalanobis distance |
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