Computation of the empirical likelihood ratio from censored data

Abstract

The empirical likelihood ratio method is a general nonparametric inference procedure that has many desirable properties. Recently, the procedure has been generalized to several settings including testing of weighted means with right-censored data. However, the computation of the empirical likelihood ratio with censored data and other complex settings is often nontrivial. We propose to use a sequential quadratic programming (SQP) method to solve the computational problem. We introduce several auxiliary variables so that the computation of SQP is greatly simplified. Examples of the computation with null hypothesis concerning the weighted mean are presented for right- and interval-censored data.

Keywords:

• Sequential quadratic programming
• Maximization
• Constraints
• Wilks' theorem

Acknowledgements

I would like to thank Arne Bathke and an anonymous referee for careful reading of this article and many suggestions that led to a clearer presentation.