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From |
"Cruces,GA (pgr)" <G.A.Cruces@lse.ac.uk> |

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

Subject |
st: "Weighted" least squares |

Date |
Mon, 8 Sep 2003 19:53:37 +0100 |

Dear All, I am trying to solve a relatively simple estimation problem that implies negative "weights" (more on my weights below), but as long as it is possible I want to use some variable transformation to use Stata's standard commands. My question, then, refers to the best way of estimating this type of problems, with or without Stata's variations of regress. I have read Stata's documentation for weights, but I am a bit confused about the distinction (if any) between "OLS with weights", which is what Stata does, and "Weighted OLS", which is what I need... Regarding Weighted OLS and my objective function for minimization, see for instance: http://www.itl.nist.gov/div898/handbook/pmd/section4/pmd432.htm The problems I need to solve are variations of least squares of the form: (1) argmin(a,b)E[Ki(Yi-a-bXi)^2] (linear OLS if all Ki=1) (2) argmin(a,b)E[Ki(Yi-F(a-bXi))^2] (probit if all Ki=1) with Ki being positive and negative, and: (3) argmin(a,b)E[Ki*So(Yi-a-bXi)^2] (qreg if Ki=1) (So is the objective function for the qreg problem). with positive Kis. These Ki are what I (and the web reference above) call weights. My first idea was a creative use of i/aweights, or variable transformations, but after a discussion with Stata Support, and discussions from this list, I think it does not work. Solving the problem for (1) is not too hard, shouldn't be too hard for (2), and I don't know where to start with (3), but ideally I would like to know if there is a general approach to solving the problem of minimizing Ki*(y-Fi[x])^2... Regarding the powerful "nl" procedure, although similar to what I want to do, I have a problem because my weights can be negative: nl finds b to minimize Sum_j (u_j^2), with: y_j = f(X_j,b) + u_j What I need to do is find b to minimize Sum_j [(Ki)*(u_j^2)]... Thank you very much for your help best, guillermo * * 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/

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