Heteroscedastic semiparametric transformation models: estimation and testing for validity

TL;DR

This paper introduces a heteroscedastic transformation model with nonparametric regression and variance functions, providing estimation methods, hypothesis tests for model validity, and a bootstrap approach, supported by simulation results.

Contribution

It develops estimators for the transformation parameter, regression, and variance functions, and proposes tests for model validity with asymptotic and bootstrap inference.

Findings

Estimators are asymptotically normal.

Tests have known limiting distributions.

Simulation confirms good small sample performance.

Abstract

In this paper we consider a heteroscedastic transformation model, where the transformation belongs to a parametric family of monotone transformations, the regression and variance function are modelled nonparametrically and the error is independent of the multidimensional covariates. In this model, we first consider the estimation of the unknown components of the model, namely the transformation parameter, regression and variance function and the distribution of the error. We show the asymptotic normality of the proposed estimators. Second, we propose tests for the validity of the model, and establish the limiting distribution of the test statistics under the null hypothesis. A bootstrap procedure is proposed to approximate the critical values of the tests. Finally, we carry out a simulation study to verify the small sample behavior of the proposed estimators and tests.