Optimal rate of convergence for nonparametric change-point estimators for nonstationary sequences

Annals of Statistics

Volumn 35, Issue 4, 2007, Pages 1802-1826

  Ben Hariz, Samir ^a   Wylie, Jonathan J ^b   Zhang, Qiang ^b  

^a UNIVERSITÉ DU MAINE   (France)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Consistency; Long range dependence; Nonparametric change point estimation; Nonstationary sequences; Rates of convergence; Short range dependence

Indexed keywords

EID: 41849138696     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053606000001596     Document Type: Article

References (15)

1. ARCONES, M. A. (1994). Limit theorems for nonlinear functionals of a stationary Gaussian sequence of vectors. Ann. Probab. 22 2242-2274.
2. BEN HARIZ, S. and WYLIE, J. J. (2005). Rates of convergence for the change-point estimator for long-range dependent sequences. Statist. Probab. Lett. 73 155-164.
3. BROCKWELL, P. J. and DAVIS, R. A. (1991). Time Series: Theory and Methods, 2nd ed. Springer, New York.
4. CARLSTEIN, E. (1988). Nonparametric change-point estimation. Ann. Statist. 16 188-197.
5. CSÖRGOCOMBINING DOUBLE ACUTE ACCENT, M. and HORVÁTH, L. (1997). Limit Theorems in Change-Point Analysis. Wiley, Chichester.
6. DÜMBGEN, L. (1991). The asymptotic behavior of some nonparametric change-point estimators. Ann. Statist. 19 1471-1495.
7. FERGER, D. (1994). On the rate of almost sure convergence of Dümbgen's change-point estimators. Statist. Probab. Lett. 19 27-31.
8. FERGER, D. (2001). Exponential and polynomial tailbounds for change-point estimators. J. Statist. Plann. Inference 92 73-109.
9. FERGER, D. (2004). Boundary estimation based on set-indexed empirical processes. J. Nonparametr. Statist. 16 245-260.
10. GIRAITIS, L., LEIPUS, R. and SURGAILIS, D. (1996). The change-point problem for dependent observations. J. Statist. Plann. Inference 53 297-310.
11. HORVÁTH, L. and KOKOSZKA, P. (1997). The effect of long-range dependence on changepoint estimators. J. Statist. Plann. Inference 64 57-81.
12. KOKOSZKA, P. and LEIPUS, R. (1998). Change-point in the mean of dependent observations. Statist. Probab. Lett. 40 385-393.
13. MÓRICZ, F. (1976). Moment inequalities and the strong laws of large numbers. Z. Wahrsch. Verw. Gebiete. 35 299-314.
14. VAN DER VAART, A. and WELLNER, J. A. (1996). Weak Convergence and Empirical Processes. With Applications to Statistics. Springer, New York.
15. YAO, Y.-C., HUANG, D. and DAVIS, R. A. (1994). On almost sure behavior of change-point estimators. In Change-Point Problems (E. Carlstein, H.-G. Müller and D. Siegmund, eds.) 359-372. IMS, Hayward, CA.