Nonanticipating estimation applied to sequential analysis and changepoint detection

Annals of Statistics

Volumn 33, Issue 3, 2005, Pages 1422-1454

  Lorden, Gary ^a   Pollak, Moshe ^b  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

Cusum; Gamma distribution; Nonlinear renewal theory; Power one tests; Quality control; Renewal theory; Shiryayev Roberts; Statistical process control; Surveillance

Indexed keywords

EID: 23744436154     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053605000000183     Document Type: Article

References (19)

1. DRAGALIN, V. P. (1997). The sequential change point problem. Economic Quality Control 12 95-122.
2. LAI, T. L. and SIEGMUND, D. (1977). A nonlinear renewal theory with applications to sequential analysis. I. Ann. Statist. 5 946-954.
3. LORDEN, G. and POLLAK, M. (1994). An alternative to mixtures for sequential testing and changepoint detection. Technical report.
4. POLLAK, M. (1978). Optimality and almost optimality of mixture stopping rules. Ann. Statist. 6 910-916.
5. POLLAK, M. (1987). Average run lengths of an optimal method of detecting a change in distribution. Ann. Statist. 15 749-779.
6. POLLAK, M. and SIEGMUND, D. (1975). Approximations to the expected sample size of certain sequential tests. Ann. Statist. 3 1267-1282.
7. POLLAK, M. and SIEGMUND, D. (1991). Sequential detection of a change in a normal mean when the initial value is unknown. Ann. Statist. 19 394-416.
8. POLLAK, M. and YAKIR, B. (1999). A simple comparison of mixture vs. nonanticipating estimation. Sequential Anal. 18 157-164.
9. ROBBINS, H. and SIEGMUND, D. (1972). A class of stopping rules for testing parametric hypotheses. Proc. Sixth Berkeley Symp. Math. Statist. Probab. 4 37-41. Univ. California Press, Berkeley.
10. ROBBINS, H. and SIEGMUND, D. (1974). The expected sample size of some tests of power one. Ann. Statist. 2 415-436.
11. ROBERTS, S. W. (1966). A comparison of some control chart procedures. Technometrics 8 411-430.
12. SHIRYAYEV, A. N. (1963). On optimum methods in quickest detection problems. Theory Probab. Appl. 8 22-46.
13. SIEGMUND, D. (1985). Sequential Analysis: Tests and Confidence Intervals. Springer, New York.
14. SIEGMUND, D. (1986). Boundary crossing probabilities and statistical applications. Ann. Statist. 14 361-404.
15. SIEGMUND, D. and VENKATRAMAN, E. S. (1995). Using the generalized likelihood ratio statistic for sequential detection of a change-point. Ann. Statist. 23 255-271.
16. STONE, C. (1965). On moment generating functions and renewal theory. Ann. Math. Statist. 36 1298-1301.
17. WOODROOFE, M. (1982). Nonlinear Renewal Theory in Sequential Analysis. SIAM, Philadel-phia.
18. YAKIR, B. (1995). A note on the run length to false alarm of a change-point detection policy. Ann. Statist. 23 272-281.
19. YAKIR, B. and POLLAK, M. (1998). A new representation for a renewal-theoretic constant appearing in asymptotic approximations of large deviations. Ann. Appl. Probab. 8 749-774.