[R] MLE for a t distribution

[Kjetil Halvorsen]

Brian Ripley sometimes on this list or elsewhere suggested to
reparametrize as 1/k. I have used that with good results. But you
should be aware that
usually data contains very little information about k, so thhat
if you do not have a lot more than 100 observations you coukld
be out of luck. You should try to plot the likelihood as a function of k,
possibly also the profile likelihood.

Kjetil

On Thu, Dec 10, 2009 at 6:06 PM, Barbara Gonzalez
<barbara.p.gonzalez at gmail.com> wrote:
> Thank you.
>
> I actually found fitdistr() in the package MASS, that "estimates" the
> df, but it does a very bad job. I know that the main problem is that
> the t distribution has a lot of local maxima, and of course, when
> k->infty we have the Normal distribution, which has nice and easy to
> obtain MLEs.
>
> I will try re-parametrizing k, but I doubt this will solve the problem
> with the multiple local maxima.
>
> I would like to implement something like the EM algorithm to go around
> this problem, but I don't know how to do that.
>
> Barbara
>
> On Thu, Dec 10, 2009 at 2:59 PM, Albyn Jones <jones at reed.edu> wrote:
>> k -> infinity gives the normal distribution.  You probably don't care
>> much about the difference between k=1000 and k=100000, so you might
>> try reparametrizing df on [1,infinity) to a parameter on [0,1]...
>>
>> albyn
>>
>> On Thu, Dec 10, 2009 at 02:14:26PM -0600, Barbara Gonzalez wrote:
>>> Given X1,...,Xn ~ t_k(mu,sigma) student t distribution with k degrees
>>> of freedom, mean mu and standard deviation sigma, I want to obtain the
>>> MLEs of the three parameters (mu, sigma and k). When I try traditional
>>> optimization techniques I don't find the MLEs. Usually I just get
>>> k->infty. Does anybody know of any algorithms/functions in R that can
>>> help me obtain the MLEs? I am especially interested in the MLE for k,
>>> the degrees of freedom.
>>>
>>> Thank you!
>>>
>>> Barbara
>>>
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>>
>
> ______________________________________________
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> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>