Bias, variance, and MSE as a function of bandwidth: Consider the artificial regression function introduced in the preceding exercise. Using Equation 18.1 (page 537), write down expressions for the...

Bias, variance, and MSE as a function of bandwidth: Consider the artificial regression function introduced in the preceding exercise. Using Equation 18.1 (page 537), write down expressions for the expected value and variance of the local-linear estimator as a function of the bandwidth h of the estimator. Employing these results, compute the variance, bias, and mean-squared error of the local-linear estimator at the focal value x₀
= 10 as a function of h, allowing h to range between 1 and 20. What value of h produces the smallest MSE? Does this agree with the optimal bandwidth h*(10) from Equation 18.2? Then, using Equation 18.2, graph the optimal bandwidth h*(10) as a function of the focal value x₀, allowing x₀
to range between 0 and 100. Relate the resulting function to the regression function.