Double stepwise likelihood ratio test for one-sided composite hypotheses

Abstract

In this paper, we propose a novel sequential test for one-sided composite hypotheses based on a stepwise likelihood ratio statistics. Its stopping boundaries are constant and can be easily determined by our provided searching algorithm. The theoretical results in this paper show that our proposed test satisfies two type error constraints and has a finite stopping time. The simulation studies show that our proposed test combines the advantages of the SPRT and the 2-SPRT and minimizes expected sample size in pointwise. To illustrate the proposed test, a real example is analyzed.

Keywords:

• 2-SLRST
• SLRS
• 2-SPRT
• SPRT
• sequential test
• power 1 test
• type I error
• type II error
• one-sided composite hypotheses

Acknowledgements

The authors wish to thank the editor, the associate editor and the anonymous referees for numerous insightful comments which improve the paper greatly.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Science Fund of China [grant number 11501209], [grant number 11271135], [grant number 11471119], [grant number 71402133]; the Postdoctoral Science Foundation of China [2014M560317], [2015M570348]; the Fundamental Research Funds for the Central Universities and the 111 Project [B14019]; Shanghai Rising Star Program 16QA1401700; Project of Shanghai Universities to enhance the competition and innovation “collaborative innovation of modern statistical methods and theory”.