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A geometric property of the sample mean and residuals

Author

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  • Kagan, Abram M.
  • Yu, Tinghui

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.

Suggested Citation

  • Kagan, Abram M. & Yu, Tinghui, 2009. "A geometric property of the sample mean and residuals," Statistics & Probability Letters, Elsevier, vol. 79(11), pages 1409-1413, June.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:11:p:1409-1413
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    Cited by:

    1. Kagan, Abram M. & Malinovsky, Yaakov, 2013. "Monotonicity in the sample size of the length of classical confidence intervals," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 78-82.

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