0

I know that Khinchin's Law is for sample mean: $$\overline X_n=\cfrac 1n\sum_{i=1}^{n}{X_i}$$ $$\lim _{n \rightarrow \infty} \operatorname{Pr}\{\left|\overline{X}_n-\mu\right|<\varepsilon\}=1$$

How to get a law for sample variance: $$S^2_n=\cfrac{1}{n-1}\sum_{i=1}^{n}(X_i-\overline X_n)^2=\cfrac{1}{n-1}(\sum_{i=1}^{n}X_i^2-n\overline X^2_n)$$ $$\lim _{n \rightarrow \infty} \operatorname{Pr}\{\left|S^2_n-\sigma^2\right|<\varepsilon\}=1$$

chaosink
  • 111
  • 1
    If you know the fourth moment is finite then https://stats.stackexchange.com/questions/316714/sampling-distribution-of-sample-variance-of-non-normal-iid-r-v-s might help – Henry Apr 19 '23 at 02:24

0 Answers0