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Topic: Reducing bias of a Bayesian point estimator
Replies: 13   Last Post: Oct 19, 2012 3:02 AM

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paulvonhippel at yahoo

Posts: 72
Registered: 7/13/05
Re: Reducing bias of a Bayesian point estimator
Posted: Oct 18, 2012 6:19 PM
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On Thursday, October 18, 2012 8:13:11 AM UTC-5, David Jones wrote:
> "Paul" wrote in message
>
> news:a9bda0dc-b6c3-4105-a9c6-d1af75e58d2e@googlegroups.com...
>

> > > > i.e.,
>
> >
>
> >
>
> > Many of the usual frequentist techniques for bias adjustment would lead
>
> > to estimates not obeying your bound. If you were not insisting on not
>
> > allowing a value of gamma exactly equal to one then the obvious thing to
>
> > start from
>
> > would be a simple truncation at 1. You might consider truncating at a
>
> > value slightly smaller than one if an exact-1 causes problems. Otherwise
>
> > you
>
> > might be able to base something on he following....
>
> >
>
> > (a) let T be the non-truncated version of the estimated for gamma;
>
> >
>
> > (b) the transformed estimate S=T/(1+T) should have good properties if the
>
> > true value of gamma is small, and is forced to lie in the required
>
> > interval;
>
> >
>
> > (c) consider the extended set of estimates S=T/(1+T^a)^(1/a), which are
>
> > again forced to lie in 0 to 1, and choose a for good properties
>
> >
>
> > Other families of transformed estimates might be considered.
>
>
>
> This is an intriguing possibility except that what I need is an estimator
>
> that performs well if the true value of gamma is large (close to 1) not
>
> small.
>
>
>
> --------------------------------------------------------------------------------
>
>
>
> The basis here is that such an approach starts from an estimating function
>
> that has good properties both for small gamma, and for large (since the
>
> estimators are constrained to be close to 1 if the raw sample estimate is
>
> large). It is not clear how much can be achieved analytically, but a
>
> minimum might be to use an estimator S=bT/(1+bT), and choose b to that the
>
> bias is correct to a low order in a power series expansion in terms of
>
> gamma. This would notionally spread the good property of the estimator near
>
> zero, away from zero to some unknown extent ... you might hope to get an
>
> explicit formula for a value of b in terms of your sample size N.
>
> Alternatively, you might allow a clipped estimator S= min(1, bT) and see
>
> what arises ... you might get some formulae in terms of incomplete gamma
>
> functions, valid for any gamma, and then see if you are happy with the
>
> result for gamma=1. You were not clear whether a value for the estimator
>
> exactly equal to one causes problems (for your confidence intervals)...
>
> which is a different question from whether gamma=1 is valid within the
>
> model.


Thank you. I haven't seen estimators of the form S=bT/(1+bT) before. Is there a name for that class of estimators? Perhaps I should read more about it.

An estimate of 1 for gamma is unfortunately not usable, though I have experimented with estimators of the form S= min(1-e, bT) where e is small.



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