Estimation of a semiparametric transformation model

Details Estimation of a semiparametric transformation model Estimation of a semiparametric transformation model

2008-04-04

arxiv.org/abs/0804.0719v1

Annals of Statistics 2008, Vol. 36, No. 2, 686-718

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/009053607000000848 the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053607000000848

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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