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When is the inverse regression estimator MSE-superior to the standard regression estimator in multivariate controlled calibration situations?

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  • Sundberg, Rolf

Abstract

We assume as model a standard multivariate regression of y on x, fitted to a controlled calibration sample and used to estimate unknown x's from observed y-values. The standard weighted least squares estimator ('classical', regress y on x and 'solve' for x) and the biased inverse regression estimator (regress x on y) are compared with respect to mean squared error. The regions are derived where the inverse regression estimator yields the smaller MSE. For any particular component of x this region is likely to contain 'most' future values in usual practice. For simultaneous estimation this needs not be true, however.

Suggested Citation

  • Sundberg, Rolf, 1985. "When is the inverse regression estimator MSE-superior to the standard regression estimator in multivariate controlled calibration situations?," Statistics & Probability Letters, Elsevier, vol. 3(2), pages 75-79, April.
    • Handle: RePEc:eee:stapro:v:3:y:1985:i:2:p:75-79
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    Cited by:

    1. Lin, Chun-Sui & Huang, Mong-Na Lo, 2010. "Optimal designs for estimating the control values in multi-univariate regression models," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1055-1066, May.

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