🚀 go-pugleaf

>>>>> "Herman" == Herman Rubin <hrubin@pop.stat.purdue.edu> writes:

Herman> Even from the classical standpoint, the traditional chi-squared
Herman> test is wrong.  The distribution of the chi-squared statistic
Herman> should not have the full reduction in degrees of freedom for
Herman> estimated parameters.  This was proved by Chernoff and Lehmann in
Herman> 1953 for fixed partitions, and by A. R. Roy in his dissertation
Herman> under me in 1954 for data-defined partitions; the theory using
Herman> "good" estimators under the null hypothesis shows that it does not
Herman> matter how the partitions are defined.  Some of the papers of D. H.
Herman> Moore about 1970 provide a readable summary.

That's an interesting point, and I would just like to add a small comment.
If you reduce the data to panel frequencies and estimate the parameters
from the resulting multinomial likelihood then the asymptotic chi-squared
distribution must indeed be correct.  The catch is, of course, that no-one
ever does this, and the reduction to frequencies is not a sufficiency
reduction, so it would be inefficient so to do.

Herman> For a discussion of testing from a parametric robust Bayesian
Herman> viewpoint, readers may wish to look at my paper with Sethuraman in
Herman> Sankhya, 1965, on the subject.

I shall.  But I seem dimly to remember a paper by Anscombe on the subject
in the JRSS(?) yonks ago.  Does anyone else recall this?  (It may be
referenced in Herman's paper, of course; I think Anscombe was pre 1965.)

Herman> But one thing to keep in mind--the higher the dimension, the more
Herman> important the assumptions.

Amen.
--
___________________________________________________________________________
Bill Venables, Dept. of Statistics, | Email: venables@stats.adelaide.edu.au
Univ. of Adelaide, South Australia. | Tel: +61 8 228 5412  Fax: ...232 5670