What is the convergence rate for Monte-Carlo variance estimate for a random variable $X \in {L^q}(\Omega ,R),2 < q < 4$?
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I think you need to be more specific in what exactly you are looking for if you want to get answers here. – Wolfgang Bangerth Dec 23 '11 at 18:13
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@Wolfgang Bangerth, I'm looking for a convergence rate in terms of number of samples. For example, for random variable with the forth moment variance estimate converges as M^(1/2), where M is the number of samples. – learningmath Dec 25 '11 at 21:49
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2Right. What I meant is: In what norm are you measuring convergence? How do you draw samples for infinite dimensional objects? Etc. – Wolfgang Bangerth Jan 02 '12 at 04:53