[R] estimating degrees of freedom iof student t

Prof Brian D Ripley ripley at stats.ox.ac.uk
Tue Jun 6 13:30:32 CEST 2000

```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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