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From |
"Mark Schaffer" <M.E.Schaffer@hw.ac.uk> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: RE: Numerical maximization |

Date |
Fri, 4 Oct 2002 18:19:33 +0100 |

Al, Nick, Thanks for the advice! Cheers, Mark From: "FEIVESON, ALAN H. (AL) (JSC-SD) (NASA)" <alan.h.feiveson1@jsc.nasa.gov> To: "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu> Subject: st: RE: Numerical maximization Date sent: Fri, 4 Oct 2002 10:47:22 -0500 Send reply to: statalist@hsphsun2.harvard.edu > Mark - > > If you want to find a value of x that maximizes an arbitrary funcrion > f(x), you might be able to fool -nl- into doing it, provided you can > bound the function. Here's how. Suppose you know f(x) < f0 for all x. > Then create a dummy data set with two observations as follows: clear > set obs 2 gen y=1000 in 1/*(the value of f0)*/ replace y=0 in 2 /* it > doesn't matter what y is on obs. 2 as long as it's different from f0 > */ nl max y y > > > The last command calls Stata's nonlinear least square -nl- program. To > use it you have to write your own nl-program. Here's an example where > you are trying to maximize f(x)=x*(x+2)*exp(-0.5*x)/(x+1) for x > 0. > > program define nlmax > > if "`1'" == "?" { > global S_1 " Z " > global Z= 1 > exit > } > cap gen fh=. > global X=exp($Z) > replace fh=$X*(2+$X)*exp(-.5*$X)/(1+$X) in 1 > replace fh=`2' in 2 > > replace `1' = fh > > end > > What this is doing is finding a value of Z = log(x) that makes f(x) > come as close to 1000 as possible. Since 1000 is an upper bound on > f(x), this will maximize f. Use of log(x) instead of x prevents the > consideration of negative values. For example this function has a > vertical asymptote at x = -1. > > Hope this helps. > > Al Feiveson > > > > > > > > -----Original Message----- > From: Mark Schaffer [mailto:M.E.Schaffer@hw.ac.uk] > Sent: Wednesday, October 02, 2002 11:09 AM > To: statalist@hsphsun2.harvard.edu > Subject: st: Numerical maximization > > > Hi everybody. A very general question for you: > > What's the recommended strategy if you're writing a Stata estimator > that requires numerical maximization methods but isn't maximum > likelihood? And if you think you might want to make the estimator > available for general use? > > Stata doesn't have a maximize program as such (-maximize- seems to be > an ML program ... but maybe it's good enough for the task?). -findit- > told me about a couple of user-written programs called -amoeba- and > -quasi-. I have no experience with these, nor with the tradeoffs in > writing code that rely on other people's routines. (It's great that > they make their code publicly available, but we can't expect them to > refrain from changing the specs if they see fit to do so, and of > course that could cause your own code to fail to work.) > > --Mark > > Prof. Mark E. Schaffer > Director > Centre for Economic Reform and Transformation > Department of Economics > School of Management & Languages > Heriot-Watt University, Edinburgh EH14 4AS UK > 44-131-451-3494 direct > 44-131-451-3008 fax > 44-131-451-3485 CERT administrator > http://www.som.hw.ac.uk/cert > * > * For searches and help try: > * http://www.stata.com/support/faqs/res/findit.html > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > * > * For searches and help try: > * http://www.stata.com/support/faqs/res/findit.html > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ Prof. Mark E. Schaffer Director Centre for Economic Reform and Transformation Department of Economics School of Management & Languages Heriot-Watt University, Edinburgh EH14 4AS UK 44-131-451-3494 direct 44-131-451-3008 fax 44-131-451-3485 CERT administrator http://www.som.hw.ac.uk/cert * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: RE: Numerical maximization***From:*"FEIVESON, ALAN H. (AL) (JSC-SD) (NASA)" <alan.h.feiveson1@jsc.nasa.gov>

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