Austin,
The ridge is everywhere... the model has ancillary parameters not
identified under the null. Davies-Hansen-Andrews-Ploberger story, if
you know what I mean (see some links at
http://www.citeulike.org/user/ctacmo/tag/identification if you're
interested). So in population I have an exactly flat ridge. What I
have in the sample is of course a mystery of small samples, but at any
rate it is not nice. Re-parameterization won't help much, although I
have several options to play with.
Partha,
yes, that's pretty much the same problem as identification in FMM.
There, if you test H0: N(0,1) vs. H1: (1-\theta) N(0,1) + \theta
N(\mu,1), then \theta\mu = 0 under the null, and you cannot identify
both parameters. The numeric derivatives are based on subtracting one
sampling zero from another (O(1/\sqrt{n}), I think), so now wonder
they are quite unstable. So your insight, although not great, is
exactly relevant :)). Probably I cannot just do any better in this
model.
--
Stas Kolenikov, also found at http://stas.kolenikov.name
Small print: I use this email account for mailing lists only.
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