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arXiv · 0804.0719

Estimation of a semiparametric transformation model

Oliver Linton·Stefan Sperlich·Ingrid Van Keilegom
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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.

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Oliver Linton, Stefan Sperlich, Ingrid Van Keilegom. 2008-04-04. Estimation of a semiparametric transformation model. https://doi.org/10.1214/009053607000000848

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