Spring Seminar Series - January 19, 2006
University of Minnesota
School of Statistics
College of Liberal Arts
Estimation
of a Semiparametric Transformation Model
Ingrid van Keilegom
Department of Statistics
Universite Catholique de Louvain, Belgium
Thursday, January 19, 2006
3:30 PM, 115
Ford Hall
Minneapolis, East Bank Campus
Social at 3:00 PM, 300 Ford Hall
Abstract
We
propose consistent estimators for transformation parameters in
semiparametric models. The problem is to find the optimal
transformation into the space of models with a predetermined structure.
Special cases are searching for the transformation to yield an additive
or a multiplicative nonparametric model. We do not focus on a
particular non-parametric estimator, but give results for the
estimation of the transformation when the rest of the model is
estimated non- or semi-parametrically and fulfills some consistency
conditions. For the estimation of the transformation parameter are
proposed two methods: minimizing the mean squared distance from
independence or maximizing a profiled likelihood function. First is
discussed the problem of identification of such models. We then state
results for a general class of nonparametric estimators. Finally we
give some particular examples for nonparametric estimation of
transformed separable models. The theoretical results as well as the
small sample performance are studied by several simulation exercises.
This work is joint work with Oliver Linton and Stefan Sperlich.