Truncated sequential change-point detection based on renewal counting processes

Scandinavian Journal of Statistics

Volumn 29, Issue 4, 2002, Pages 693-719

  Gut, Allan ^a   Steinebach, Josef ^b  

^a UPPSALA UNIVERSITY   (Sweden)

^b PHILIPPS UNIVERSITY MARBURG   (Germany)

Author keywords

Change point; Extreme value asymptotics; First passage time; Increments; Renewal counting process; Sequential tests; Stopping time; Strong approximation; Wiener process

Indexed keywords

EID: 0036899456     PISSN: 03036898     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9469.00313     Document Type: Article

References (24)

1. Bhattacharya, P.K. & Frierson, D. (1981). A nonparametric control chart for detecting small disorders. Ann. Statist. 9, 544-554.
2. Borodin, A. & Salminen, P. (1996). Handbook of Brownian motion-facts and formulae. Birkhäuser, Basel.
3. Csörgo, M. & Horváth, L. (1988). Nonparametric methods for changepoint problems. Handbook of statistics 7 (eds P.R. Krishnaiah and C.R. Rao), 403-425. North-Holland, Amsterdam.
4. Csörgo, M. & Horváth, L. (1993). Weighted approximations in probability and statistics. Wiley, New York.
5. Csörgo, M. & Horváth, L. (1997). Limit theorems in change-point analysis. Wiley, Chichester.
6. Csörgo, M., Horváth, L. & Steinebach, J. (1987). Invariance principles for renewal processes. Ann. Probab. 15, 1441-1460.
7. Csörgo, M. & Révész, P. (1981). Strong approximations in probability and statistics. Académiai Kiadó, Budapest.
8. Darling, D.A. & Erdos, P. (1956). A limit theorem for the maximum of normalized sums of independent random variables. Duke Math. J. 23, 143-155.
9. Deheuvels, P. & Révész, P. (1986). Weak laws for the increments of Wiener processes, Brownian bridges, empirical processes and partial sums of i.i.d.r.v.'s. Proc. 6th Pannonian Symp. Math. Stat. Prob. Theory, Bad Tatzmannsdorf, Austria, Vol. A, 69-88.
10. Gombay, E. (1995). Nonparametric truncated sequential change-point detection. Statist. Decis. 13, 71-82.
11. Gut, A. (1974). On the moments and limit distributions of some first passage times. Ann. Probab. 2, 277-308.
12. Gut, A. (1988). Stopped random walks. Springer-Verlag, New York.
13. Gut, A. & Steinebach, J.(2000). Truncated sequential change-point detection based on renewal counting processes. U.U.D.M. Report 2000:18. Uppsala University. http://www.math.uu.se/research/pub/ preprints.html.
14. Haiman, G. (1999). First passage time for some stationary processes. Stochastic Process. Appl. 80, 231-248.
15. Haiman, G. (2000). Block records and maxima of increments of the Wiener process. J. Statist. Plann. Inference 85, 137-144.
16. Horváth, L. & Steinebach, J. (2000). Testing for changes in the mean or variance of a stochastic process under weak invariance. J. Statist. Plann. Inference 91, 365-376.
17. Komlós, J., Major, P. & Tusnády, G. (1975). An approximation of partial sums of independent r.v.'s and the sample d.f., I. Z. Wahrsch. Verw. Gebiete 32, 111-131.
18. Leadbetrer, M.R., Lindgren, G. & Rootzón, H. (1983). Extremes and related properties of random sequences and processes. Springer-Verlag, New York.
19. Page, E.S. (1954). Continuous inspection schemes. Biometrika 41, 100-115.
20. Page, E.S. (1955). A test for a change in a parameter occurring at an unknown point. Biometrika 42, 523-527.
21. Steinebach, J. (1988). Invariance principles for renewal processes when only moments of low order exist. J. Multivariate Anal. 26, 169-183.
22. Steinebach, J. (1994). Change-point and jump estimates in an AMOC renewal model. In: Asymptotic statistics (eds P. Mandl & M. Hušková), 447-457. Physica-Verlag, Heidelberg.
23. Steinebach, J. (1995). Variance estimation based on invariance principles. Statistics 27, 15-25.
24. Steinebach, J. & Eastwood, V.R. (1995). On extreme value asymptotics for increments of renewal processes. J. Statist. Plann. Inference 45, 301-312.