Statistics and Data Science Seminar
Prof. Guang Cheng
Purdue University
Bootstrap Consistency for General Semiparametric M-estimation
Abstract: Consider M-estimation in a semiparametric model that is characterized by a
Euclidean parameter of interest and a nuisance function parameter. We show
that, under general conditions, the bootstrap is asymptotically consistent
in estimating the distribution of the M-estimate of Euclidean parameter;
this is, the bootstrap distribution asymptotically imitates the distribution
of the M-estimate. We also show that the bootstrap confidence set has the
asymptotically correct coverage probability. These general conclusions hold,
in particular, when the nuisance parameter is not estimable at root-n rate.
Our results provide a theoretical justification for the use of bootstrap as
an inference tool in semiparametric modelling and apply to a broad class of
bootstrap methods with exchangeable bootstrap weights. A by-product of our
theoretical development is the second order asymptotic linear expansion of
the (bootstrap) M-estimate. Joint work with Jianhua Huang at Texas A&M University.
Wednesday September 23, 2009 at 3:00 PM in SEO 636