[R] Off topic -2 Ln Lambda and Chi square

[Adelchi Azzalini]

On Mon, 11 Jul 2005 11:18:55 -0400, Liaw, Andy wrote:

LA> If you meant the lambda as the likelihood ratio test statistic, the
LA> asymptotic chi-squared distribution comes from the asymptotic
LA> normality of the MLEs.  The proof is in a paper by Abraham Wald in
LA> 1943.  See Stuart & Ord (Kendall's Advanced Statistics) for
LA> discussion (e.g., vol. 2, 5th edition).
LA> 
LA> Andy
LA> 
LA> > From: Laura Holt
LA> > 
LA> > Dear R :
LA> > 
LA> > Sorry for the off topic question, but does anyone know the 
LA> > reference for
LA> > the -2 Ln Lambda following a Chi Square distribution, please?
LA> > 

see

S. S Wilks ( 1938)
The large-sample distribution of the likelihood ratio for testing composite hypotheses
- Ann. Math. Stat, 9, 60-62

-- 
Adelchi Azzalini  <azzalini at stat.unipd.it>
Dipart.Scienze Statistiche, Università di Padova, Italia
tel. +39 049 8274147,  http://azzalini.stat.unipd.it/