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Re: [S] How can I fit a t-distribution to a sample?

To: s-news@wubios.wustl.edu
Subject: Re: [S] How can I fit a t-distribution to a sample?
From: "Christmann, Andreas" <A.Christmann@HRZ.Uni-Dortmund.DE>
Date: Wed, 31 May 2000 12:01:48 +0200
Organization: Universitaet Dortmund, HRZ
References: <H00004ac0b7c8d09@MHS>
Sender: owner-s-news@wubios.wustl.edu
>>Hi,
>>
>>How can I fit a t-distribution to a sample?

>From my point of view this is not purely an S-Plus question.
Perhaps the estimation technique most often used to fit a t-distribution is the 
maximum likelihood
method.
However it can happen (quite often if the d.f. is small) that the ML-estimate 
is not unique assuming
t-distributed errors.
Perhaps the following papers may be interesting.

E.g.
EM-algorithm
\item[] {\rm Lange, K.L., Little, R.J.A. and Taylor, J.M.G.} (1989).
  Robust statistical modelling using the t distribution.
  {\em J. Amer. Statist. Assoc.}, {\bf 84}, 881-886.

\item[] {\rm M{\"a}kel{\"a}inen, T., Schmidt, K. \& Styan, G.P.H.} (1981).
  On the existence and uniqueness of the maximum likelihood estimate of a
  vector-valued parameter in fixed-size samples.
  {\em Ann. Statist.}, {\bf 9}, 758-767.

\item[] {\rm Copas, J.B.} (1975).
  On the unimodality of the likelihood for the Cauchy distribution.
  {\em Biometrika}, {\bf 62}, 701-704.

\item[] {\rm Barnett, V.} (1966).
  Evaluation of the maximum-likelihood estimator where the
  likelihood equation has multiple roots.
  {\em Biometrika}, {\bf 53}, 151-165.

\item[] {\rm Kent, J.T. and Tyler, D.E.} (1991).
  Redescending M-estimates of multivariate location and scatter.
  {\em Ann. Statist.}, {\bf 19}, 2102-2119.
%-  Key words:
%-  redescending M-estimate
%-  robustness
%-  multivariate t-distribution

Yours sincerely,
Andreas

----------------------------------------------
A.Christmann@hrz.uni-dortmund.de

PD Dr. Andreas Christmann
Universitaet Dortmund
Hochschulrechenzentrum
Wissenschaftliche Anwendungen
D-44221 Dortmund
GERMANY
phone  (049)-231-755-2763
fax                 -2731


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