Shrinkage estimation in lognormal regression model for censored data

ABSTRACT

We introduce in this paper, the shrinkage estimation method in the lognormal regression model for censored data involving many predictors, some of which may not have any influence on the response of interest. We develop the asymptotic properties of the shrinkage estimators (SEs) using the notion of asymptotic distributional biases and risks. We show that if the shrinkage dimension exceeds two, the asymptotic risk of the SEs is strictly less than the corresponding classical estimators. Furthermore, we study the penalty (LASSO and adaptive LASSO) estimation methods and compare their relative performance with the SEs. A simulation study for various combinations of the inactive predictors and censoring percentages shows that the SEs perform better than the penalty estimators in certain parts of the parameter space, especially when there are many inactive predictors in the model. It also shows that the shrinkage and penalty estimators outperform the classical estimators. A real-life data example using Worcester heart attack study is used to illustrate the performance of the suggested estimators.

KEYWORDS:

• Asymptotic distributional bias and risk
• adaptive LASSO
• likelihood ratio test
• lognormal regression
• Monte Carlo simulation
• shrinkage estimators

Acknowledgments

We express our sincere thanks to the referees and the editor for their constructive and valuable suggestions, which led to an improvement of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of Shakhawat Hosain was supported by a grant from the Natural Sciences and Engineering Research Council of Canada and that of Hatem A. Howlader by the University of Winnipeg.