A geometric property of the sample mean and residuals

Abram M. Kagan and Tinghui Yu

Statistics & Probability Letters, 2009, vol. 79, issue 11, 1409-1413

Abstract: For a sample (x1,...,xn) from a population with finite second moment it is proved that the angle between the sample mean and the subspace generated by the residuals monotonically decreases as n increases and thus has a limit that, in the regular case, involves the Fisher information and looks rather elegant. It has a close connection to the estimation of a location parameter. Some numerical examples illustrate the result.

Date: 2009
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