Question 3

Problem 3. Let X1, . . . ,Xn be a random sample from a population with zero mean, positive variance and nite fourth moment. There are three estimators of the population variance 02, A n 2 .. A A .. Man A l X- 0H2, Hrs\" EZHZTJlX- 3:1 .7 where ilk denotes the kth sample moment 1 n A E : k [.1]: = E X3.- :1 and :\\ is as in the previous problem. (1) Derive the asymptotic distribution of all three estimators. (2) Which estimator has the smallest asymptotic variance? (3) Compare the three estimators in a simulation study. (4) \"Thich estimator do you recommend