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Can anyone provide insights on computing quantiles of a distribution using Monte Carlo simulation? I'm mainly interested in what convergence bounds are available (for any approach) and in the existence of non-standard algorithms (such as the one discussed in the paper by Dagum, Karp, Luby and Ross).

Convergence depends up on the sample that u generated. normally 10000 simulations........ Only trial and error approach and also depends upon ur interest of value(error).If you are taking about complex function like Bayesain function, then its also depends on the covering function which u choose to simulate.

Yes, it certainly depends on the number of samples. I am looking for bounds such as Chebychev's inequality, which, for the mean, gives a bound on a the likelihood that the estimator error is greater than a certain threshold, explicitly computed based on the variance, the error threshold, and the number of simulations. Are there corresponding convergence bounds for quantile estimators? I imagine that there aren't, but I wonder what is typically used in this situation.

Is "computing quantiles of a distribution using Monte Carlo simulation" different from bootstrapping quantiles?

i think there's some discussion of this in Paul Glasserman's book

I think you'll find that convergence is driven by two statistical factors:1. The probabilities of more or fewer samples falling above or below the quantile boundary which drives uncertainty about which sample or sample interval lies closest to the desired quantile boundary.2. The sampling density at the quantile boundary which is a function of N, the use of any kind of importance sampling, and the inverse of the PDF of the distribution. If you are trying to find a quantile boundary in a very thin part of the PDF (e.g. the tails or the mid-point of a deeply bimodal distribution) then you'll suffer from larger errors.

Perhaps it's the same. Can you recommend a good reference on the subject of bootstrapping quantiles? I haven't been able to pull up a good introduction searching online. QuoteOriginally posted by: PanniniIs "computing quantiles of a distribution using Monte Carlo simulation" different from bootstrapping quantiles?