Importance Sampling for Generalized Likelihood Ratio Procedures in Sequential Analysis

Abstract

This paper describes importance sampling techniques for Monte Carlo computation of the error probabilities and false alarm rates of sequential GLR (generalized likelihood ratio) tests and detection rules. It also discusses asymptotically optimal choice of the proposal distributions for importance sampling and gives numerical comparisons of the sequential GLR procedures with other sequential tests of composite hypotheses and detection rules in the literature.

Key Words:

• Generalized likelihood ratio
• Importance sampling
• Multivariate exponential family
• Sequential change-point detection
• Sequential multiple hypothesis testing

Subject Classifications:

• 62L05
• 62L10
• 65C05

ACKNOWLEDGMENT

Chan's research was supported by the National University of Singapore, and Lai's research was supported by the National Science Foundation and the National Cancer Institute. The authors express their appreciation to the referee for helpful references and comments.