On Wed, 31 May 2000, Bill Venables wrote:
>
> Your formula for the negative log-likelihood is incorrect and should be
>
> ~ -log(dt((xx - mu)/sd, df)) + log(sd)
>
> but I very much doubt that will solve the problem completely. Once the df
> parameter of the t-distribution climbs above about 8 there is really very
> little shape difference in the t family so you will most likely need
> enormous samples to fix an estimate of it.
another idea is to reparametrize - for example map df by a smooth
transformation the interval [0,1], where 1 corresponds to infinite df.
Perhaps something like
alpha = df/(c + df)
the constant c determines the df corresponding to alpha = .5. This
won't alter the fact that you won't have good estimates of df for larger
df, but it might improve things both computationally and otherwise.
albyn
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