Maximum pairwise-rank-likelihood-based inference for the semiparametric transformation model

TL;DR

This paper introduces two novel inference methods for the general linear transformation model, leveraging pairwise rank likelihood to improve robustness and efficiency over traditional kernel-smoothing and rank-only approaches.

Contribution

The paper proposes pairwise rank likelihood and score-function-based methods for the transformation model, with theoretical analysis and superior empirical performance.

Findings

Estimators are robust to error distribution.

Methods achieve comparable or smaller mean square errors.

Theoretical properties are rigorously established.

Abstract

In this paper, we study the linear transformation model in the most general setup. This model includes many important and popular models in statistics and econometrics as special cases. Although it has been studied for many years, the methods in the literature are based on kernel-smoothing techniques or make use of only the ranks of the responses in the estimation of the parametric components. The former approach needs a tuning parameter, which is not easily optimally specified in practice; and the latter is computationally expensive and may not make full use of the information in the data. In this paper, we propose two methods: a pairwise rank likelihood method and a score-function-based method based on this pairwise rank likelihood. We also explore the theoretical properties of the proposed estimators. Via extensive numerical studies, we demonstrate that our methods are appealing in that the estimators are not only robust to the distribution of the random errors but also lead to mean square errors that are in many cases comparable to or smaller than those of existing methods.