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 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.
Dr. Li’s work is supported in part by the Natural Sciences and Engineering Research Council of Canada (grant number RGPIN-2020-04964). Dr. Yu’s work is supported in part by Singapore Ministry of Education Academic Research Tier 1 Fund: A-8000413-00-00.
The authors thank the editor, the associate editor, and two referees for constructive comments and suggestions that lead to a significant improvement over the article. The first two authors contribute equally to this work.
"Maximum profile binomial likelihood estimation for the semiparametric Box–Cox power transformation model." Electron. J. Statist. 17 (2) 2317 - 2342, 2023. https://doi.org/10.1214/23-EJS2146