A rank-based empirical likelihood approach to two-sample proportional odds model and its goodness of fit

Abstract

A rank-based empirical likelihood method is proposed and applied to estimate the proportionality parameter and the underlying distributions in a two-sample semiparametric proportional odds model. A distribution-free goodness-of-fit test for the model is also given. It is proved that the maximum likelihood estimator of the proportionality parameter is reciprocal symmetric. As one of the applications, we use the proposed procedure to estimate receiver operating characteristic (ROC) curves. We also perform a simulation study to assess the performance of the proposed procedure and provide a numerical example based on real-world data to illustrate the implementation of the method.

Keywords:

• distribution-free
• goodness-of-fit test
• likelihood
• Monte Carlo method
• proportional odds model
• ranks
• reciprocal symmetry
• reliability analysis
• ROC curve
• semiparametric model
• survival data

AMS Subject Classification:

• Primary 62G05
• 62G10
• 62G15

Acknowledgements

The authors are grateful to the Editor, Associate Editor and referee for their careful reading and for a number of insightful comments and helpful suggestions that have greatly improved our original submission.