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Biometrika 1981 68(3):685-689; doi:10.1093/biomet/68.3.685
© 1981 by Biometrika Trust
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Use of regression functions for improved estimation of means

NORMAN S. MATLOFF

Division of Statistics, University of California Davis

Suppose one has a random sample from a distributionFY,X, the goal being to estimate µ, the unconditional mean of Y. If the regression function of Y on X is of a known parametric form, one might consider estimating µ by the average of the estimated regression function values at the sample points. It is shown here that such an estimator can offer substantial improvement over the sample mean of Y, and that in no case does the former estimator have larger asymptotic variance than the latter estimator. Applications of this asymptotic distribution theory to the double-sampling setting are also given.

Key Words: Double sampling • Nonlinear regression • Regression function


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