STATS 203 - Large Sample Theory - Lecture 12 (Slutsky's Thm Examples; Delta Method)

Examples of the application of the Slutsky's Theorems (in law); Asymptotic normality of the one-sample t statistic; Slutsky's Theorems in probability and almost surely; Delta Method; second-order improvement of the asymptotic distribution

[@RollingcoleW]

Thank you

[@syz911]

22:50: This is misleading. You have made an implicit assumption that Var(Xi^2) is finite. Law of large numbers work when the population variance is finite. In this case you need to prove that Var(Xi^2) is finite in order to apply the law of large numbers. Your derivation works for samples for distributions for which the fourth and second moments are finite. In general, Sn^2 is not a consistent estimator of sigma^2 unless Var(Sn^2) approaches zero at the limit.