On Wed, Jan 28, 2009 at 7:57 PM, Austin Nichols <[email protected]> wrote:
> Stas et al.--
> I think Sergiy is solving for roots of F(x)-A only, and only in the
> "nice" part of the function F(x) where x>0 and F<0 and F looks
exactly
> differentiable there. Of course, we have not actually seen the
> functional form... and plenty of functions that look smooth are
> nowhere differentiable.
F() is result of a simulation (and hence depends on the data I am
working with). The form of F() may change depending on dataset, but
monotonic decline is expected in this (positive) part. Analytical
solution in this part might be possible, but painful enough to be
avoided.
>
> I think Mata's optimizer is probably the best option for this problem,
> if one has Stata 10 --Roger Harbord says "Mata -optimize()- is also
> designed as a maximizer (or minimizer) rather than a root-finder" but
> note that Mata's optimize() can minimize (F(x)-A)^2 just fine which is
> the same as finding a root of F(x)-A. But Sergiy seems to be limited
which was exactly my original strategy: ml maximize -(F(x)-A)^2
> to Stata 9, so optimize() is not an option. I have not compared the
> performance of Ben Jann's -mm_root()- [findit moremata] to -ridder-
> [findit ridder] and I would interested to hear others' experience...
I ended up implementing a variant of the Newton's method, with
numerical evaluation of derivatives, which seems to be working. I
decided to divert from -ridder- because of it's reliance on globals
and lack of support of r() saved results (and also it's one more file
to carry with). Otherwise the method itself was working fine.
Thank you everyone that responded.
>
> Perhaps -moremata- needs a web page like -estout-...
>
> On Wed, Jan 28, 2009 at 4:51 PM, Stas Kolenikov <[email protected]> wrote:
>> One problem I see with your function is that it is not differentiable.
>> Stata's -ml maximize- and -optimize- are really intended for nice
>> smooth functions that have well separated local maxima, and when they
>> have something like yours, they get crazy estimates of derivatives
>> that would either throw the algorithm out all the time, or at least
>> make it fail to recognize the convergence point if the convergence
>> conditions involve gradients (-gtolerance- and -nrtolerance- options
>> of -maximize-). I thought Russian mathematical training was good
>> enough to teach those issues ;).
>>
>> Also, -difficult- is next to useless with 1D optimization, as far as I
>> understand it, since its main job is to break down the parameter space
>> into (almost flat) ridges and nicely convex (approximately) quadratic
>> components, so as to not invert an ill conditioned matrix for the
>> first situation.
>>
>> I'd say in situation like yours simulated annealing is the thing to go
>> with if you do minimization. If you do root finding, you would need to
>> work with a pretty rough algorithm that does not involve derivatives.
>> I don't know what -ridder- relies on, but if it converges, use the
>> answers and don't touch anything :))
>>
>> And yes, at some point I've fooled with $ML_b vector, but I would not
>> recommend doing that since you don't know exactly how -ml- uses it,
>> unless you reverse engineered everything it does. Given that you've
>> reverse engineered some of the graphics and tabulated output, I won't
>> be surprised if you did :))
>>
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