boancqu 题目如下.^2 是平方的意思. Prove that the conditional mean E(Y |X), where X is a predictor or input random variable, and Y is a response variable, minimizes the mean-squared error loss function over all regression functions g(X) E(Y − g(X))^2>= E(Y − E(Y |X))^2 谢谢了.
rtist First, carefully read this artical, http://cos.name/bbs/read.php?tid=7989. Then, write out the integral and use high-school level mathematical trick to find the minimum.
yihui 这不是学数理统计时那道经典的条件期望题么,至少Jun Shao的数上是有证明过程的,其实也很简单。先把(Y − g(X))分为两部分,(Y - E(Y |X) + E(Y |X) - g(X)),然后把平方展开,用条件期望的一些定理,就证明出来了。