Question: *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

*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 ¼ 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*ð10Þ from Equation 18.2? Then, using Equation 18.2, graph the optimal bandwidth h*ðx0Þ as a function of the focal value x0, allowing x0 to range between 0 and 100. Relate the resulting function to the regression function.

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