Re: Find a consistent estimator?

In article <4360ff0e@xxxxxxxxxxxxxx>, David Jones <dajxxx@xxxxxxxxx> wrote:
>tom wrote:
>> you mean finding the expected value of f(x/A) and then set
>> sample mean=population mean?

> You would need the expected value of X as a function of A, then set
>sample mean=population mean.


>> isn't the MLE just the derivative of log((1+Ax)/2)^n set to equal 0?
>> now i haven't calculated that yet, but why isn't it a possible
>> estimator?

>It is possible estimator, but there may be no simple explicit solution
>to the equation. You might need to have a simple explicit expression
>for the MLE to demonstrate consistency. MLE's are not always
>consistent, but you would need to find an esoteric distribution for
>the MLE not to be consistent.

It is not hard to find highly non-esoteric distributions
for which the MLE does not even exist, but the local MLE
is not only consistent, but a good estimator. A mixture
of two normals, with both mean and variance of one of them
unknown, is enough, as is the three-parameter lognormal.


--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.

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