If I have a sequence of random variable $X_n$, and $EX_n=o(\frac{1}{n}),var(X_n)=o(\frac{1}{n^4})$, is the stochastic order $X_n= o_p(\frac{1}{n})$ or $o_p(\frac{1}{n^2})$? I perfer the latter. Does it mean if I want to check the order of a random variable, I just need calculate the convergence speed of variance, and ensure the convergence of mean is engough, no matter what the convergence speed of mean?
2026-03-30 03:20:21.1774840821
which determines the order of convergence, mean or variance?
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