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RE: st: halton sequence


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: halton sequence
Date   Fri, 6 Aug 2004 22:04:41 +0100

Here's my stab at it based on that valuable 
information. 

halton, gen(h2)
halton, gen(h3) q(3) 
halton, gen(h3_15) q(3) n(15) 

*! 1.0.0 NJC 6 August 2004 
*! based on Gauss program by Daniel Feenberg and Jonathan Skinner 
*! to generate n numbers you need at least n + 1 observations 
program halton
	version 8 
	syntax , GENerate(str) [ Q(int 2) N(str)] 

	if "`n'" == "" local n = _N - 1  
	else if (`n' + 1) > _N error 2001 

	confirm new var `generate' 
	local g "`generate'" 
	tempname y x
	local np1 = `n' + 1 

	qui {
		gen double `g' = 0 
	
		forval i = 2/`np1' { 
			scalar `y' = 1/`q' 
			scalar `x' = 1 - `g'[`i' - 1]
			while `x' <= (`y' + 1e-11) {  
				scalar `y' = `y' / `q' 
			}	
			replace `g' = ///
			`g'[`i' - 1] + (`q' + 1) * `y' - 1 in `i' 
		}
		replace `g' = `g'[_n + 1] in 1/`n'   
		replace `g' = . in `np1' 
	} 	
end
	

Nick 
n.j.cox@durham.ac.uk 

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu]On Behalf Of Daniel
> Feenberg
> Sent: 06 August 2004 20:25
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: halton sequence
> 
> 
> I have actually co-authored a paper using Halton sequences, 
> but we used
> Gauss to generate them (I didn't know any Stata at the time). The full
> source for our generator is in Appendix B of the paper (
> http://www.nber.org/papers/w4147 ), and looking at it I don't 
> see why it
> couldn't be done in Stata. However my Gauss is now weak, and I may
> not be understanding my own code. 
> 
> Halton's paper describes the sequences in a number-theoretic way which
> looks like something only a LISP interpreter could do, but there is an
> alternative floating point generater that Halton also 
> describes (and which
> is referenced in our paper). We coded it in about a dozen 
> lines of Gauss.
> If you are trying to do LISP in Stata, that would be a problem.
> 
> We did find much faster convergence with Halton sequences. I 
> hope you will
> give them a try.
> 
> Daniel Feenberg
> 
> On Fri, 6 Aug 2004, Alfonso Miranda Caso Luengo wrote:
> 
> > Dear all,
> > 
> > Let me expand a little on my last e-mail. In the last few 
> years Maximum Simulated likelihood has been proposed as a 
> good alternative for estimating models where various random 
> effects are present so that maximum likelihood estimation 
> requires multivariate integration. Though Gauss-Hermite 
> integration is possible with, say, four or less random 
> effects, integration by simulation seems to be a promising 
> alternative. Integration by simulation can be based on random 
> draws from a uniform. However, it has been suggested in the 
> literature that using Halton draws (which are systematic and 
> cover better the 0-1 interval) is better. For these reasons I 
> would like to use Halton draws to write a simulated maximum 
> likelihood routine.
> > 
> > I have found however that this is not an easy task in 
> Stata, as most Halton generators currently available are 
> written in low level language on the basis of programming 
> facilities that we do not have in Stata. I am sure there is a 
> Stata way to do it, I just cannot imagine an efficient way 
> (all my ideas crash with the length limits of macros and 
> matrices in Stata). 

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