Estimation of a semiparametric transformation model
Abstract
This paper proposes consistent estimators for transformation parameters in semiparametric models. The problem is to find the optimal transformation into the space of models with a predetermined regression structure like additive or multiplicative separability. We 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. We propose two methods for the estimation of the transformation parameter: maximizing a profile likelihood function or minimizing the mean squared distance from independence. First the problem of identification of such models is discussed. We then state asymptotic results for a general class of nonparametric estimators. Finally, we give some particular examples of nonparametric estimators of transformed separable models. The small sample performance is studied in several simulations.
Cite
@article{arxiv.0804.0719,
title = {Estimation of a semiparametric transformation model},
author = {Oliver Linton and Stefan Sperlich and Ingrid Van Keilegom},
journal= {arXiv preprint arXiv:0804.0719},
year = {2008}
}
Comments
Published in at http://dx.doi.org/10.1214/009053607000000848 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)