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利用回归函数改进均值估计AI 解读

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…

利用回归函数改进均值估计AI 解读

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…