Kink estimation with correlated noise

Journal of the Korean Statistical Society

Volumn 38, Issue 2, 2009, Pages 131-143

  Wishart, Justin ^a  

^a UNIVERSITY OF SYDNEY   (Australia)

Author keywords

62G05; 62G20; Change point; Climate change; Fractional Gaussian noise; Fractional integration; High order kernel; Inverse problems; Kink; Long range dependence; primary; secondary; Separation rate lemma; Zero crossing technique

Indexed keywords

EID: 63349110771     PISSN: 12263192     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jkss.2008.08.001     Document Type: Article

References (32)

1. Abry P., and Veitch D. Wavelet analysis of long-range-dependent traffic. IEEE Transactions on Information Theory 44 1 (1998) 2-15
2. Antoch J., Hušková M., and Prášková Z. Effect of dependence on statistics for determination of change. Journal of Statistical Planning and Inference 60 2 (1997) 291-310
3. Beran J. Statistical methods for data with long-range dependence. Statistical Science 7 4 (1992) 404-416
4. Beran J. Statistics for long-memory processes. Monographs on statistics and applied probability Vol. 61 (1994), Chapman and Hall, New York
5. Brown L.D., and Low M.G. Asymptotic equivalence of non-parametric regression and white noise. The Annals of Statistics 24 6 (1996) 2384-2398
6. Cavalier L. Estimation in a problem of fractional integration. Inverse Problems 20 5 (2004) 1445-1454
7. Cheng M., and Raimondo M. Kernel methods for optimal change-points estimation in derivatives. Journal of Computational & Graphical Statistics 17 1 (2008) 56-75
8. Csörgö S., and Mielniczuk J. Nonparametric regression under long-range dependent normal errors. The Annals of Statistics 23 3 (1995) 1000-1014
9. Davies R.B., and Harte D.S. Tests for Hurst effect. Biometrika 74 1 (1987) 95-101
10. Gijbels I., and Goderniaux A.-C. Bootstrap test for change-points in non-parametric regression. Journal of Nonparametric Statistics 16 3-4 (2004) 591-611
11. Gijbels I., and Goderniaux A.-C. Data-driven discontinuity detection in derivatives of a regression function. Communications in Statistics and Theory Methods 33 4 (2004) 851-871
12. Gijbels I., Hall P., and Kneip A. On the estimation of jump points in smooth curves. Annals of the Institute of Statistical Mathematics 51 2 (1999) 231-251
13. Goldenshluger A., Tsybakov A., and Zeevi A. Optimal change-point estimation from indirect observations. The Annals of Statistics 34 1 (2006) 350-372
14. Gripenberg G., and Norros I. On the prediction of fractional Brownian motion. Journal of Applied Probability 33 2 (1996) 400-410
15. Huh J., and Carrière K.C. Estimation of regression functions with a discontinuity in a derivative with local polynomial fits. Statistics & Probability Letters 56 3 (2002) 329-343
16. Huh J., and Park B.U. Detection of a change point with local polynomial fits for the random design case. Australian & New Zealand Journal of Statistics 46 3 (2004) 425-441
17. Johnstone I.M. Wavelet shrinkage for correlated data and inverse problems: Adaptivity results. Statistica Sinica 9 1 (1999) 51-83
18. Johnstone I.M., and Silverman B.W. Wavelet threshold estimators for data with correlated noise. Journal of the Royal Statistical Society Series B 59 2 (1997) 319-351
19. Korostelëv A.P. Minimax estimation of a discontinuous signal. Teoriya Veroyatnosteǐ iee Primeneniya 32 4 (1987) 796-799
20. Korostelëv A.P., and Tsybakov A.B. Minimax theory of image reconstruction. Lecture notes in statistics Vol. 82 (1993), Springer-Verlag, New York
21. p-wavelet regression with correlated errors and inverse problems. Statistica Sinica (in press)
22. Mandelbrot B.B., and Van Ness J.W. Fractional Brownian motions, fractional noises and applications. SIAM Review 10 (1968) 422-437
23. Müller H.-G. Change-points in non-parametric regression analysis. The Annals of Statistics 20 2 (1992) 737-761
24. Pickands III J. Asymptotic properties of the maximum in a stationary Gaussian process. Transactions on American Mathematical Society 145 (1969) 75-86
25. Raimondo M. Minimax estimation of sharp change points. The Annals of Statistics 26 4 (1998) 1379-1397
26. Raimondo M., and Tajvidi N. A peaks over threshold model for change-point detection by wavelets. Statistica Sinica 14 2 (2004) 395-412
27. Tang S.M., and MacNeill I.B. The effect of serial correlation on tests for parameter change at unknown time. The Annals of Statistics 21 1 (1993) 552-575
28. Veitch D., and Abry P. A wavelet-based joint estimator of the parameters of long-range dependence. IEEE Transactions on Information Theory 45 3 (1999) 878-897
29. Wang Y. Jump and sharp cusp detection by wavelets. Biometrika 82 2 (1995) 385-397
30. Wang Y. Function estimation via wavelet shrinkage for long-memory data. The Annals of Statistics 24 2 (1996) 466-484
31. Wang Y. Minimax estimation via wavelets for indirect long-memory data. Journal of Statistical Planning and Inference 64 1 (1997) 45-55
32. Wang Y. Change-points via wavelets for indirect data. Statistica Sinica 9 1 (1999) 103-117