Estimation of a semiparametric transformation model

TL;DR

This paper develops consistent methods for estimating transformation parameters in semiparametric models, enabling optimal data transformation for models with additive or multiplicative structures, supported by asymptotic theory and simulations.

Contribution

It introduces two novel estimation techniques for transformation parameters in semiparametric models, with theoretical guarantees and practical performance evaluation.

Findings

Consistent estimators for transformation parameters are proposed.

Asymptotic properties of the estimators are established.

Simulation studies demonstrate the estimators' effectiveness.

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.