Apologies for several similar earlier postings on GLS - I wasn't
sure that any had gone thru'. I'm bringing this posting to the top.
My request is for a procedure that will estimate k that
will maximize the log-likelihood function, being a function of the
residual sum of squares viz [y(i)/w(i)-1/w(i)-x(i)/w(i)]^2, as w(i)
is a function of k (see below for previous post)!
Come on you Stata coders, someone can surely help. Thanks.
Also, in reply to Professor Stephen P. Jenkins, once k is known Var
[(n(i)] can be backed out.
--- In [email protected], "easycalcs" <easycalcs@y...> wrote:
> There's no need at the estimation stage to know the variance of e
(i)
> or n(i):
>
> Substititute for b(i) in the original y equation
>
> y = b0+Bx(i)+v(i)
>
> where v(i)=e(i)+x(i)n(i)
>
> The new equation has a heteroskedastic error
> Var[v(i)]= Var[e(i)]+x(i)^2Var[(n(i)] = Var[e(i)]{1+kx(i)^2}
> where k= Var[e(i)]/Var[n(i)]
>
> If e(i) and n(i) are iid ~ normally, a loglikelihood formulation
can
> be set up. If the weights are computed as w(i)=(1+kx(i))^1/2 the
> weighted least squares is y(i)/w(i) on 1/w(i) and x(i)/w(i). A
> concentrated loglikelihood may be established (with unknown
paramter
> k) where the residual sum of (weighted) least is formulated in
terms
> of the unknown parameter k. This is then maximised wrt k!
>
> Does anyone have the formulation/Stata specification proc for such
a
> concentrated loglikelihood function? I'm not a Stata coder! Thanks.
>
> GM,Reading(aka easycalcs)
>
>
> --- In [email protected], "Stephen P. Jenkins"
> <stephenj@e...> wrote:
> > On Mon, 20 Oct 2003 12:54:33 -0400 Steven Devaney
> > <DevaneySP@n...> wrote:
> >
> > > Hello again
> > >
> > > Off-list I was asked to clarify what I meant.
> > >
> > > What I am interested in is whether anyone knows about or has
> written an MLE procedure for estimating B in the set-up?
> > >
> > > y(i) = b0 + b1(i) + e(i)
> > >
> > > where
> > >
> > > b1(i) = B + n(i)
> > >
> > > I was hoping to use Hildreth and Houck, but cannot constrain
> xtrchh so that t = 1.
> >
> > If t = 1 (single cross-section), can you identify the variance of
> the
> > b1(i), or equivalently the variance of the n(i) ?
> >
> >
> > Stephen
> > ----------------------
> > Professor Stephen P. Jenkins <stephenj@e...>
> > Institute for Social and Economic Research (ISER)
> > University of Essex, Colchester, CO4 3SQ, UK
> > Tel: +44 (0)1206 873374. Fax: +44 (0)1206 873151.
> > http://www.iser.essex.ac.uk
> >
> > *
> > * 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:
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> * http://www.ats.ucla.edu/stat/stata/
*
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