R help - Jun 2000 - estimating degrees of freedom iof student t

I have come across the following situation when using the function 
pt which calls the student t distribution function. I simulate data 
from a normal distribution and fit the student t. The estimated 
degrees of freedom gets  larger at each iteration and there is no 
convergence. It seems there should be some mechanism where it 
switched to a normal distribution when the degrees of freedom gets 
very large.
Gabrielle Kelly
Dept. of Statistics
National University of Ireland Dublin.

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On Tue, 6 Jun 2000 gabrielle.kelly at ucd.ie wrote:
> I have come across the following situation when using the function 
> pt which calls the student t distribution function. I simulate data 
> from a normal distribution and fit the student t. The estimated 
> degrees of freedom gets  larger at each iteration and there is no 
> convergence. It seems there should be some mechanism where it 
> switched to a normal distribution when the degrees of freedom gets 
> very large.
(There is: pt switches at n = 4e5 to a normal approximation, although a
more accurate one than N(0, 1). It's in the source code
.../src/nmath/pt.c.)

I think you need to tell us a bit more: there is nothing in R that I know
of to estimate the parameters of a t distribution.  If you are using
maximum likelihood, there is no guarantee that I know of that the
likelihood has a global maximum, let alone a unique one.  It is entirely
possible that the normal is a better fit that any t.  I would
transform the space, and optimize over 1/nu constrained to [0, 0.5], I
think.  (For nu == 1 all sorts of thing go wrong.)

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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