Estimation of a semiparametric transformation model

Linton, Oliver ; Sperlich, Stefan ; Van Keilegom, Ingrid

Ann. Statist., Tome 36 (2008) no. 1, p. 686-718 / Harvested from Project Euclid

Résumé

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.

Détail

Publié le : 2008-04-15
Classification:  Additive models,  generalized structured models,  profile likelihood,  semiparametric models,  separability,  transformation models,  62E20,  62F12,  62G05,  62G08,  62G20