Sequential detection of transient signal by moving likelihood ratio statistic in an exponential family

ABSTRACT

We first consider the sequential detection of transient signals by generalizing the moving average chart to exponential family and study the false detection probability (FDP) and power of detection (POD) in the steady state. Then windowed adjusted signed (or modified directed) likelihood ratio chart is studied by treating it as approximate normal random variable. In the multi-parameter exponential family, the detection of the transient change of one of the canonical parameters or a function of canonical parameters is considered by using the generalized adjusted signed likelihood ratio chart. Comparisons with window restricted CUSUM and Shiryayev-Roberts (S-R) procedures show that the generalized signed likelihood ratio chart performs quite well. Several important examples including the mean or variance change under normal model and a real-time example are used for illustration.

KEYWORDS:

• Exponential family
• adjusted signed likelihood ratio
• approximate false detecting probability
• power of detection
• moving average procedure

Acknowledgments

This work was done when the author was visiting Department of Statistics of Stanford University. Many discussions with Professor D. Siegmund and comments from Professor N. Reid are very helpful. Comments and suggestions from three referees and an associate editor greatly improved the presentation and are appreciated.