We know that $S^{2}$ is an unbiased estimator of $\sigma^{2}$ and $S$ is a biased estimator of $\sigma$. But if $n\rightarrow\infty$, then $S$ is an asymptotically unbiased estimator of $\sigma$. I found a proof here. But in the last step, instead of solving the limit, graphic visualization has been given. Can we somehow algebraically prove that bias$\rightarrow0$ as $n\rightarrow\infty$?
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Cross-posted at https://math.stackexchange.com/q/3759687/321264. – StubbornAtom Jul 17 '20 at 20:29
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Yes, I was confused whether I should post in calculus or statistics. After initially posting on this channel and getting no replies. I thought it was more of a calculus based question rather than statistics. So, later I posted it on Math Stack exchange. – Puneet Jul 18 '20 at 01:55
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Is there a rule regarding which question can be posted where? I am new to Stack Exchange. – Puneet Jul 18 '20 at 01:55