Monday, September 25, 2000
Communications 120 at 3:30 P.M.
Jon Wellner:
"Maximum Likelihood Estimators and LR Statistics
for some Non-Regular Problems: Monotone and Convex Functions"
For regular statistical problems it is well-known that maximum
likelihood estimators have asymptotically normal distributions, and
likelihood ratio statistics are asymptotically chi-square. For
non-regular problems these classical limit distributions fail to hold.
In this talk I will briefly discuss recent progress concerning the
asymptotic distribution theory of maximum likelihood estimators and
likelihood ratio statistics for a class of non-regular problems
connected with estimation of a monotone or convex function. For
monotone functions, the limiting distributions can be described in
terms of the slope (process) of the greatest convex minorant of
two-sided Brownian plus a parabola. For convex functions, the
limiting distributions are described in terms of a certain
``invelope'' of two-sided integrated Brownian motion +t4. I
will also mention a few of the many open problems connected with this
area of research.
Russell Steele:
"Bayes Factors for Finite Mixture Models from the EM
Algorithm via Importance Sampling."
We present a general method for calculating the Bayes factors for finite
mixture models via importance sampling of the mixture component labels.
The importance sampling function uses conditional group probabilities
obtained via the EM algorithm and the complete data-likelihood to sample
from vital regions of the parameter space. The integration method
requires less computational time than Markov Chain Monte
Carlo and is far easier to implement, involving only
sampling from multinomial distributions and from the prior.
Refreshments to follow in the Statistics lounge, 3rd floor, Padelford.
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