Open Access
2023 Maximum profile binomial likelihood estimation for the semiparametric Box–Cox power transformation model
Pengfei Li, Tao Yu, Baojiang Chen, Jing Qin
Author Affiliations +
Electron. J. Statist. 17(2): 2317-2342 (2023). DOI: 10.1214/23-EJS2146

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 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.

Funding Statement

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.

Acknowledgment

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.

Citation

Download Citation

Pengfei Li. Tao Yu. Baojiang Chen. Jing Qin. "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

Information

Received: 1 March 2022; Published: 2023
First available in Project Euclid: 4 October 2023

MathSciNet: MR4649983
Digital Object Identifier: 10.1214/23-EJS2146

Subjects:
Primary: 62N99
Secondary: 62N02

Keywords: Binomial likelihood , Box–Cox transformation , Empirical processes , M-estimation , semiparametric inference , U-processes

Vol.17 • No. 2 • 2023
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