Maximum profile binomial likelihood estimation for the semiparametric Box--Cox power transformation model

TL;DR

This paper introduces a new semiparametric estimation method for the Box--Cox transformation model that is robust to unknown error distributions and performs well compared to existing techniques.

Contribution

The paper proposes a maximum profile binomial likelihood approach for the semiparametric Box--Cox model, with theoretical distribution results and superior empirical performance.

Findings

Method outperforms existing methods when error distribution deviates from normal.

Theoretical joint distribution of estimators is established.

Demonstrated effectiveness on HIV data set.

Abstract

The Box--Cox transformation model has been widely applied for many years. The parametric version of this model assumes that the random error follows a parametric distribution, say the normal distribution, and estimates the model parameters using the maximum likelihood method. The semiparametric version assumes that the distribution of the random error is completely unknown; existing methods either need strong assumptions, or are less effective when the distribution of the random error significantly deviates from the normal distribution. We adopt the semiparametric assumption and propose a maximum profile binomial likelihood method. We theoretically establish the joint distribution of the estimators of the model parameters. Through extensive numerical studies, we demonstrate that our method has an advantage over existing methods, especially when the distribution of the random error deviates from the normal distribution. Furthermore, we compare the performance of our method and existing methods on an HIV data set.