Parametric Conditional Mean Estimator Gauss file(s) npr_parametric.g Matlab file(s) npr_parametric.m Simulate the following model for T = 500 observations yt = 0.3 exp(−4(xt + 1)2 ) + 0.7 exp(−16(xt − 1)2 ) + ut , where ut ∼ N(0, 0.1) and xt ∼ U [−2, 2] .

(a) Estimate the conditional mean of the linear model yt = β0 + β1xt + vt .

(b) Estimate the conditional mean of the quartic polynomial model yt = β0 + β1xt + β2x 2 t + β3x 3 t + β4x 4 t + vt .

(c) Compare the conditional mean estimates in parts

(a) and

(b) with the true conditional mean m(x) = 0.3 exp(−4(x + 1)2 ) + 0.7 exp(−16(x − 1)2 ). Also compare your results with Figure 11.5.