Spring Seminar Series - March 24, 2005
University of Minnesota
School of Statistics
College of Liberal Arts
Monte Carlo Inference for Semiparametric Models
Michael Kosorok
Department of Statistics and Biostatistics & Medical Informatics
University of Wisconsin-Madison
Thursday, March 24, 2005
3:30 PM, 115
Ford Hall
Minneapolis, East Bank Campus
Social at 3:00 PM, 300 Ford Hall
Abstract
Semiparametric
models consist of an easily interpreted parametric component
plus a nonparametric "nuisance" component. The astounding flexibility
of
these models makes them ideal for many statistical applications,
including
econometrics, survival analysis and genetics. In this talk, we consider
two Monte Carlo methods for frequentist inference on the parametric
component separately from the nuisance parameter. Both methods are
useful when the nuisance parameter is not estimable at the parametric
rate.
The first method is based on sampling from the posterior of the
profile likelihood. It is proved that this procedure gives a first
order correct approximation to the limiting distribution of the maximum
likelihood estimator when the model is correctly specified. The method
is essentially
automatic and avoids the need to compute derivatives, either
analytically or numerically.
The second method is the weighted bootstrap applied to semiparametric
M-estimators. The approach is much more broadly applicable than the
first method but more computationally intense. The likelihood need not
be correctly specified, and certain penalized M-estimators are
eligible.
The basic idea is to used bounded weights in the bootstraps so that the
entropy numbers of the function classes involved are preserved.
Several examples will be given for both methods, along with a
discussion of how the new methods relate to existing methods, including
semiparametric
likelihood ratio statistics, semiparametric Bayesian methods, the $m$
within $n$ bootstrap, and subsampling.