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Jun 14 at 1:58 comment added Iosif Pinelis @GregZitelli : I think you are right about $2+\delta$. I had to use $4$ because it is the smallest order of the absolute empirical moment available in your setting.
Jun 13 at 23:22 comment added Greg Zitelli The choice of M is very good. I think a similar statement can be proved if $E_n |X_i|^{2+\delta}$ are bounded with high probability, here you used convergence of $E_n X_i^4$.
Jun 13 at 23:19 vote accept Greg Zitelli
Jun 10 at 22:03 history edited Iosif Pinelis CC BY-SA 4.0
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Jun 10 at 21:30 history edited Iosif Pinelis CC BY-SA 4.0
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Jun 10 at 21:11 history answered Iosif Pinelis CC BY-SA 4.0