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.

Locations

• The Annals of Statistics - View - PDF
• arXiv (Cornell University) - View - PDF
• GoeScholar The Publication Server of the Georg-August-Universität Göttingen (Georg-August-Universität Göttingen) - View - PDF
• DataCite API - View