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 $n^{-1/2}$: http://en.wikipedia.org/wiki/Quasi-Monte_Carlo_method.
However, the above article also states that the QMC numbers are not truly random, so I wonder what the implications might be for any statistical tests I might want to run on the results.
1.) What are the pros and cons of MC vs. QMC. (Would you always want to use QMC if it's 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.
There are other low discrepancy numbers, such as Sobol sequence also available in Matlab, and again I'd like to know what tests I can use to ascertain which is best for my situation.