Minimax Methods for Multihypothesis Sequential Testing and Change-Point Detection Problems

Abstract

In this paper a unified methodological approach to sequential testing of many composite hypotheses and multi-decision change-point detection for composite alternatives is proposed. New performance measures for methods of hypotheses testing and change-point detection are introduced. Theoretical lower bounds for these performance measures are proved that do not depend on methods of sequential testing and detection. Minimax tests are proposed for which these lower bounds are attained asympototically as decision thresholds tend to infinity. Results of Monte Carlo experiments are given.

Keywords:

• Asymptotically optimal tests
• Change-point problems
• Composite hypotheses testing
• Sequential analysis

Subject Classification:

• 62L10
• 62L15
• 62L99

ACKNOWLEDGMENTS

We are grateful to N. Mukhopadhyay, A. Tartakovsky, and S. Zacks for a useful discussion during our talks at the first international workshop on sequential methodology (Auburn, July 2007).

Notes

Recommended by Nitis Mukhopadhyay