Exercice 2

Mean squared prediction errors

Consider the problem of predicting Y using a function g of X, where X and Y are (possibly dependent) random variables. We want to minimize the mean squared error (MSE):

E [(Y − 9(X))²] .

We will look at various choices of g, in the particular case where Y = X³ + Z², where X and Z are independent Normal variables with mean 0 and variance 1