Open Access
August 2019 Maximum likelihood estimation in transformed linear regression with nonnormal errors
Xingwei Tong, Fuqing Gao, Kani Chen, Dingjiao Cai, Jianguo Sun
Ann. Statist. 47(4): 1864-1892 (August 2019). DOI: 10.1214/18-AOS1726


This paper discusses the transformed linear regression with non-normal error distributions, a problem that often occurs in many areas such as economics and social sciences as well as medical studies. The linear transformation model is an important tool in survival analysis partly due to its flexibility. In particular, it includes the Cox model and the proportional odds model as special cases when the error follows the extreme value distribution and the logistic distribution, respectively. Despite the popularity and generality of linear transformation models, however, there is no general theory on the maximum likelihood estimation of the regression parameter and the transformation function. One main difficulty for this is that the transformation function near the tails diverges to infinity and can be quite unstable. It affects the accuracy of the estimation of the transformation function and regression parameters. In this paper, we develop the maximum likelihood estimation approach and provide the near optimal conditions on the error distribution under which the consistency and asymptotic normality of the resulting estimators can be established. Extensive numerical studies suggest that the methodology works well, and an application to the data on a typhoon forecast is provided.


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Xingwei Tong. Fuqing Gao. Kani Chen. Dingjiao Cai. Jianguo Sun. "Maximum likelihood estimation in transformed linear regression with nonnormal errors." Ann. Statist. 47 (4) 1864 - 1892, August 2019.


Received: 1 August 2016; Revised: 1 May 2018; Published: August 2019
First available in Project Euclid: 21 May 2019

zbMATH: 07082273
MathSciNet: MR3953438
Digital Object Identifier: 10.1214/18-AOS1726

Primary: 62F12

Keywords: Linear transformation model , maximum likelihood estimation

Rights: Copyright © 2019 Institute of Mathematical Statistics

Vol.47 • No. 4 • August 2019
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