Hello,
perhaps the following article may be interesting:
\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.
It is mainly concentrated on the maximum likelihood approach.
The authors show that it can be very difficult (if the data set is
not huge) to estimate the degrees of freedom parameter
from the t-distribution with reasonable precision.
Often it seems to be better to define this
parameter to a small fixed constant , say 3 or 4, at least from
a robustness point of view.
Andreas Christmann
weidong zhang wrote:
> Hello All,
>
> I have a question on robust linear mixed model with t distributiont model
> and need your help.
>
> Suppose my linear mixed model is y = xb + zu + e, where b is a vector
> fixed effects and u is a vector of random effect. Here u ~ N(0,
> sigma_u^2), and e ~ t(0, sigma_e^2, v), where v is the degree of freedom
> of t. This assumption can also be writen as e ~ N(0, (1/w) * sigma_e^2), w
> ~ Gamma(v/2, v/2).
>
> I know there is a bayesian version to estimate v, but I wonder what is the
> simpler way to get an APPROXIMATION of v?
>
> Thanks in advance.
>
> Weidong
>
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PD Dr. Andreas Christmann
Universitaet Dortmund
Hochschulrechenzentrum
Wissenschaftliche Anwendungen
D-44221 Dortmund
GERMANY
email A.Christmann@hrz.uni-dortmund.de
phone (049)-231-755-2763
fax (049)-231-755-2731
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