Estimation Evaluation Criterion: In order to evaluate your estimation or prediction, we also generated 200 random realizations of Y's for each combination of (X1, X2) in the testing data set. However, we will not release these 200 independent realizations for the testing data. Instead we will use them to compute a baseline estimation of Abase(X1, X2) and Vbase(X1, X2) for the testing data. Specifically, for each given combination of (X1, X2), we have 200 realizations of Y's in (1), denoted by Y1, . .., Y200, and then we compute the baseline estimations based on the Monte Carlo simulations: 200 Hbase = Y - fit ...+ Y200 200 and base = Var (Y) = 200 - 1 E(Y - Y)2. i=1 Your predicted mean or variance functions, say, A(X1, X2) and V(X1, X2), will then be evaluated as compared to the baseline Monte Carlo estimations, As(X1, X2) and Vis(X1, X2): MSE, IJ EE(i(thi, 12;) - Mbase (1 1i, 12;))2 i=1 j=1 MSEv = 1 I J IJ EE(V(Ili, 121) - Vbase (Thi, 12;))?, (2) i=1 j=1 where (I, J) = (50,50) for the testing data