RE: st: halton sequence

 From "Nick Cox" <[email protected]> To <[email protected]> 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
[email protected]

> -----Original Message-----
> From: [email protected]
> [mailto:[email protected]]On Behalf Of Daniel
> Feenberg
> Sent: 06 August 2004 20:25
> To: [email protected]
> 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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