Analysis of change-point estimators under the null hypothesis

Bernoulli

Volumn 7, Issue 3, 2001, Pages 487-506

  Ferger, Dietmar ^a  

^a DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Berry esseen estimates; Change point estimation; Contiguous alternatives; Limiting null distribution; Maximizer of weighted brownian bridges; Sets of cluster points

Indexed keywords

EID: 0142140776     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.2307/3318498     Document Type: Article

References (29)

1. Andersen, E.S. (1953) On the fluctuations of sums of random variables, I. Math. Scand., 1, 263-285.
2. Antoch, J. and Huskova, M. (1999) Estimators of changes. In S. Ghosh (ed.), Asymptotics, Nonparametrics and Time Series. A tribute to Mandan Lal Pun, pp. 533-578. New York: Marcel Dekker.
3. Bhattacharya, P.K. (1987) Maximum likelihood estimation of a change-point in the distribution of independent random variables: general multiparameter case. J. Multivariate Anal, 23, 183-208.
4. Bhattacharya, P.K. and Brockwell, P.J. (1976) The minimum of an additive process with applications to signal estimation and storage theory. Z. Wahrscheinlichkeitstheorie Venv. Geb., 37, 51-75.
5. Bhattacharya, P.K. and Frierson, D. Jr (1981) A nonparametric control chart for detecting small disorders. Ann. Statist., 9, 544-554.
6. Billingsley, P. (1968) Convergence of Probability Measures. New York: Wiley.
7. Borodin, A.N. and Salminen, P. (1996) Handbook of Brmvnian Motion - Facts and Formulae. Basel: Birkhäuser.
8. Borovkov, A.A. (1973) On the rate of convergence for the invariance principle. Theory Probab. Appl., 18, 207-225.
9. Brodsky, B.E. and Darkhovsky, B.S. (1993) Nonparametric Methods in Change-point Problems. Dordrecht: Kluwer.
10. Chung, K.L. (1974) A Course on Probability Tlieory, 2nd edition. New York: Academic Press.
11. Csörgö, M. and Horvâth, L. (1988) Invariance principles for change-point problems. J. Multivariate Anal., 27, 151-168.
12. Csörgö, M. and Horvâth, L. (1993) Weighted Approximations in Probability and Statistics. New York: Wiley.
13. Csörgö, M. and Horvâth, L. (1997) Limit Theorems in Change Point Analysis. New York: Wiley.
14. Diimbgen, L. (1991) The asymptotic behavior of some nonparametric change-point estimators. Ann. Statist., 19, 1471-1495.
15. Ferger, D. (1994a) Change-point estimators in case of small disorders. J. Statist. Plann. Inference, 40, 33-49.
16. Ferger, D. (1994b) On exact rates of convergence in functional limit theorems for U-statistic type processes. J. Tlieoret. Probab., 7, 709-723.
17. Ferger, D. (1994c) On the power of nonparametric change-point tests. Metrika, 41, 277-297.
18. Ferger, D. (1995) The joint distribution of the running maximum and its location of Z)-valued Markov processes. J. Appl. Probab., 32, 842-845.
19. Ferger, D. (1996) On the asymptotic behavior of change-point estimators in case of no change with applications to testing. Statist. Decisions, 14, 137-143.
20. Ferger, D. (1999) On the uniqueness of maximizers of Markov-Gaussian processes. Statist. Probab. Lett., 45, 71-77.
21. Ferger, D. (2001) Exponential and polynomial tailbounds for change-point estimators. J. Statist. Plann. Inference, 92, 73-109.
22. Ferger, D. and Stute, W. (1992) Convergence of change-point estimators. Stochastic Process. Appl., 42, 345-351.
23. Gänssler, P. and Stute, W. (1977) Wahrscheinlichkeitstheorie. Berlin: Springer-Verlag.
24. Gombay, E. and Horvâth, L. (1996) Approximations for the time of change and the power function in change-point models. J. Statist. Plann. Inference, 52, 43-66.
25. Huskovâ, M. (1996) Tests and estimators for the change-point problem based on A/-statistics. Statist. Decisions, 14, 115-136.
26. Lombard, F. and Hart, J.D. (1994) The analysis of change-point data with dependent errors. In E. Carlstein, H.G. Mueller and D. Siegmund (eds), Change-point Problems, IMS Lecture Notes Monogr. Ser., Vol. 23, pp. 194-209. Hayward, CA: Institute of Mathematical Statistics.
27. Oosterhoff, J. and van Zwet, W.R. (1979) A note on contiguity and Hellinger distance. In J. Jureckovâ (ed.) Contributions on Statistics: Jaroslav Hâjek Memorial Volume, pp. 157-166. Dordrecht: Reidel.
28. Shorack, G.R. and Wellncr, J.A. (1986) Empirical Processes with Applications to Statistics. New York: Wiley.
29. Szyszkovicz, B. (1991) Changepoint problems and contiguous alternatives. Statist. Probab. Lett., 11, 299-308.