Specification tests in semiparametric transformation models - a multiplier bootstrap approach

TL;DR

This paper introduces a multiplier bootstrap method for specification testing in semiparametric transformation models, providing asymptotically valid, computationally efficient tests that outperform existing methods.

Contribution

It proposes a novel multiplier bootstrap approach for testing in transformation models that remains unaffected by pre-estimation, unlike previous methods.

Findings

The tests are asymptotically pivotal and have a known distribution.

The bootstrap procedure is easier to implement and less computationally intensive.

Simulation results show superior performance compared to existing methods.

Abstract

We consider semiparametric transformation models, where after pre-estimation of a parametric transformation of the response the data are modeled by means of nonparametric regression. We suggest subsequent procedures for testing lack-of-fit of the regression function and for significance of covariables, which - in contrast to procedures from the literature - are asymptotically not influenced by the pre-estimation of the transformation. The test statistics are asymptotically pivotal and have the same asymptotic distribution as in regression models without transformation. We show validity of a multiplier bootstrap procedure which is easier to implement and much less computationally demanding than bootstrap procedures based on the transformation model. In a simulation study we demonstrate the superior performance of the procedure in comparison with the competitors from the literature.