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st: Estimating a nonlinear model

From   Steve Dolado <>
Subject   st: Estimating a nonlinear model
Date   Fri, 29 Jun 2012 12:17:28 -0400

I have a model of the following form

M(y,X)= u  (u is the error term, y is the "dependent"variable and X is
a vector of regressors

I cannot isolate y here, so I guess nl will not work here.
More specifically,  the model is quadratic in the error term, so I can write

y + A(X1)*u  + B(X2)*u^2 = 0

Hence, I can write the solution in the form M(y,X)= u  by solving a
quadratic equation

u =( - A(X1) + (A(X1)^2 - 4*B(X2)*y) ^ 0.5)/(2*B(X2))


u =( - A(X1) - (A(X1)^2 - 4*B(X2)*y) ^ 0.5)/(2*B(X2))

where X1 and X2 are subsets of X with possibly overlapping components

Any idea how to estimate this model would be appreciated

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