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From |
A J van der Vlist <vlist001@hotmail.com> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
RE: st: programming in stata - problems with optimize |

Date |
Wed, 3 Aug 2011 20:48:07 +0200 |

Hi Matthew and Christophe, The objective at the beginning contained a typo indeed: it should be normal(mu-Xbeta_i) as in my code. Your suggestions do work out! Thanks indeed, Arno ---------------------------------------- > Date: Sun, 24 Jul 2011 11:37:14 +0200 > Subject: Re: st: programming in stata - problems with optimize > From: ck.statalist@gmail.com > To: statalist@hsphsun2.harvard.edu > > As Matthew points out your objective function seems to be ill-behaved. > It looks like you are trying to solve the normal equations but not > quite. Moreover the code of your objective function is not consistent > with the formula you give at the beginning of your post. Optimize > helps you finding the maximum or minimum of a function and is not > originally designed for finding the roots of an equation. However the > methods used to optimize functions, like Newton-Raphson are > root-finding methods. They find the roots of the gradient of the > objective function and this why Matthew proposes to optimize the > square of your function. You can also think of the GMM method where > the solution of the problem is solved by mimizing a quadratic form of > the moments. The problem with this method is that you have to find the > primitive of the equation you want to solve. Therefore a way to use > optimize as a root-finder is to specify the gradient, which will in > this case be equal to the equation you are trying to solve and use the > d1 evaluator. The solution will be the set of paramaters which > annulate the gradient. > > I give here an example > > I want to find mu such that Sum_{i} (x_i-mu) = 0 -> which solution I > know is the mean > > clear * > set obs 1000 > > drawnorm x > > sum x > > > mata: > > x=st_data(.,"x") > > void myf(todo,p, x, f,g,H) > { > > f=0 // obejctive function is irrelevant in this case > > if (todo==1) { > g=quadcolsum((x:-p)) // the equation I want to solve, > implicitly set equal to zero > } > > > } > > > S = optimize_init() > optimize_init_evaluator(S, &myf()) > optimize_init_evaluatortype(S, "d1") > optimize_init_params(S, (1)) > optimize_init_argument(S, 1, x) > p=optimize(S) > p > end > > > sum x // should be equal to p > > Now let's say I want to solve for x the equation x^2-2x+1=0 > > Write then > > void myf2(todo,p,f,g,H) > { > > f=0 > > if (todo==1) { > g=p^2-2*p+1 > } > > } > > > S = optimize_init() > optimize_init_evaluator(S, &myf2()) > optimize_init_evaluatortype(S, "d1") > optimize_init_params(S, (1)) > > p=optimize(S) > > p > You will find that p=1. > > You might also have a look at Benn Jann's root finder from his moremata package. > Christophe > > > 2011/7/22 A.J van der Vlist <vlist001@hotmail.com>: > > Dear Statalisters, > > > > I encouter problems in optimizing function f: > > > > I would like to solve for mu: > > > > sum over i { Nx_i' * (mu - Xbeta_i) } = Sk > > > > Nx = [n x 1] , vector of {1/n}'s in order to sum over i > > mu = parameter > > Xbeta = [n x 1] vector of fitted values > > Sk = scalar > > > > This is what I tried: > > > > scalar Sk1=Sm1_SRA > > mata: > > X=st_data(.,"Xbeta") > > Nx=st_data(.,"Nxi") > > void mymodelb(todo, mu2, f, g, H) > > { > > external Nx, X > > hlp=(mu2 :- X) > > f = (Nx' * normal(hlp)) - Sk1 > > } > > S = optimize_init() > > optimize_init_evaluator(S, &mymodelb()) > > optimize_init_params(S, 0) > > mu2 = optimize(S) > > problem: > > > > 1) I get problems when running with Sk1 in f > > 2) when I substitute for Sk1 =0.501 in f the code will give a result - yet unreasonable high +e11 > > > > Suggestions are very welcome. > > > > Arno > > * > > * For searches and help try: > > * http://www.stata.com/help.cgi?search > > * http://www.stata.com/support/statalist/faq > > * http://www.ats.ucla.edu/stat/stata/ > > > > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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