Estimation of a semiparametric transformation model. (English) Zbl 1133.62029

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

Ann. Stat. 36, No. 2, 686-718 (2008).

Summary: 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.

MSC:

62G08	Nonparametric regression and quantile regression
62G05	Nonparametric estimation
62G20	Asymptotic properties of nonparametric inference
62E20	Asymptotic distribution theory in statistics
62F12	Asymptotic properties of parametric estimators

Keywords:

additive models; generalized structured models; profile likelihood; semiparametric models; separability; transformation models

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