34. The mean squared error of an estimator Ô is MSE (Ô) = E(ô – ĝ)². If Ô is unbiased, then MSE(Ô) = V(Ô), but in general MSE(Ô) = V(Ô) + (bias)². Consider the estimator ²=KS2, where S² = sample variance. What value of K minimizes the mean squared error of this estima- tor when the population distribution is normal? [Hint: It can be shown that E[(S²)²] = (n + 1)σơ³/(n − 1) In general, it is difficult to find Ô to minimize MSE(Ô), which is why we look only at unbiased estimators and minimize V().]
34. The mean squared error of an estimator Ô is MSE (Ô) = E(ô – ĝ)². If Ô is unbiased, then MSE(Ô) = V(Ô), but in general MSE(Ô) = V(Ô) + (bias)². Consider the estimator ²=KS2, where S² = sample variance. What value of K minimizes the mean squared error of this estima- tor when the population distribution is normal? [Hint: It can be shown that E[(S²)²] = (n + 1)σơ³/(n − 1) In general, it is difficult to find Ô to minimize MSE(Ô), which is why we look only at unbiased estimators and minimize V().]
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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