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Mean squared error and selection in multivariate calibration

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  • Brown, P. J.
  • Spiegelman, C. H.

Abstract

Consider multivariate linear calibration of a single standard. We show that a selection of the q' most informative of the q responses gives a finite mean squared error for the generalised least squares prediction of an unknown standard provided 1 [less-than-or-equals, slant] q' [less-than-or-equals, slant] q and q [greater-or-equal, slanted] 3. Furthermore, the prediction mean is finite provided 1 [less-than-or-equals, slant] q' [less-than-or-equals, slant] q and q [greater-or-equal, slanted] 2 and in general the rth absolute moment exists for 1 [less-than-or-equals, slant] q' [less-than-or-equals, slant] q [greater-or-equal, slanted] r + 1. These results extend those of Lieftinck-Koeijers (1988) to the selection of responses and also sharpen her results when selection is not present, since she showed only that the mean is finite for q [greater-or-equal, slanted] 3 and the mean squared error finite for q [greater-or-equal, slanted] 5.

Suggested Citation

  • Brown, P. J. & Spiegelman, C. H., 1991. "Mean squared error and selection in multivariate calibration," Statistics & Probability Letters, Elsevier, vol. 12(2), pages 157-159, August.
    • Handle: RePEc:eee:stapro:v:12:y:1991:i:2:p:157-159
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    Cited by:

    1. Krishnamoorthy, K. & Johnson, Darren J., 1997. "Combining Independent Information in a Multivariate Calibration Problem," Journal of Multivariate Analysis, Elsevier, vol. 61(2), pages 171-186, May.

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    Keywords

    Calibration;

    Statistics

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