I want to use Quasi Monte Carlo to try and improve the convergence of a simulation I am running.
The random numbers are simply to produce the observation errors for a standard linear regression model. Which is then estimated using a number of different regression techniques. This is done repeatedly to estimate the mean square error of each model.
I'm fairly new to Quasi Monte Carlo but is is likely to help in this situation I am just using it to produce 10k random numbers. It seems that generally I can expect quicker convergence of the order of (1/n) rather than n^(-0.5):
However it also states that the QMC numbers are not truly random, so I just wonder what the implications might be for any statistical tests I might want to run on the results.
1.) I guess what I want to know are the pros and cons of MC v QMC. (would you always want to use QMC if its available?) 2.) What tests can I use to ascertain which is best for my application? (seems any test that depends on the numbers being truly random will fail?)
I know that this can be done in Matlab using
q = qrandstream('halton',NSteps,'Skip',1e3,'Leap',1e2); RandMat = qrand(q,NRepl); z_RandMat = norminv(RandMat,0,1);
which is taken from this paper.
It seems there are other low discrepancy numbers such as Sobol sequence available in Matlab and again would just like to know what tests I can use to ascertain which is best for my situation.