What is the convergence rate for Monte-Carlo variance estimate for a random variable $X \in {L^q}(\Omega ,R),2 < q < 4$?

  • $\begingroup$ I think you need to be more specific in what exactly you are looking for if you want to get answers here. $\endgroup$ Commented Dec 23, 2011 at 18:13
  • $\begingroup$ @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. $\endgroup$ Commented Dec 25, 2011 at 21:49
  • 2
    $\begingroup$ Right. What I meant is: In what norm are you measuring convergence? How do you draw samples for infinite dimensional objects? Etc. $\endgroup$ Commented Jan 2, 2012 at 4:53


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