Semiparametric inference for partially linear regressions with Box-Cox transformation

TL;DR

This paper develops a semiparametric inference method for partially linear regression models with Box-Cox transformations, balancing parametric and nonparametric approaches, and introduces new estimation and inference techniques.

Contribution

It extends the SmoothMD approach to handle Box-Cox transformed dependent variables with infinite-dimensional nuisance parameters in a semiparametric setting.

Findings

The proposed estimator is asymptotically normal.

Simulation results demonstrate good finite-sample performance.

The method effectively handles heteroskedasticity and complex transformations.

Abstract

In this paper, a semiparametric partially linear model in the spirit of Robinson (1988) with Box- Cox transformed dependent variable is studied. Transformation regression models are widely used in applied econometrics to avoid misspecification. In addition, a partially linear semiparametric model is an intermediate strategy that tries to balance advantages and disadvantages of a fully parametric model and nonparametric models. A combination of transformation and partially linear semiparametric model is, thus, a natural strategy. The model parameters are estimated by a semiparametric extension of the so called smooth minimum distance (SmoothMD) approach proposed by Lavergne and Patilea (2013). SmoothMD is suitable for models defined by conditional moment conditions and allows the variance of the error terms to depend on the covariates. In addition, here we allow for infinite-dimension nuisance parameters. The asymptotic behavior of the new SmoothMD estimator is studied under general conditions and new inference methods are proposed. A simulation experiment illustrates the performance of the methods for finite samples.