Use of regression functions for improved estimation of means
Norman Matloff · Biometrika · 1981
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.