Improved sizer for time series

Statistica Sinica

Volumn 19, Issue 4, 2009, Pages 1511-1530

  Park, Cheolwoo ^a   Hannig, Jan ^b   Kang, Kee Hoon ^c  

^a UNIVERSITY OF GEORGIA   (United States)

^b University of North Carolina at Chapel Hill   (United States)

^c Hankuk University of Foreign Studies   (South Korea)

Author keywords

Autocovariance function estimation; Local linear smoothing; Multiple testing adjustment; Sizer; Statistical convergence; Time series

Indexed keywords

EID: 69249232870     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. Berman, S. M. (1964). Limit theorems for the maximum term in stationary sequences. Ann. Math. Statist. 35, 502-516.
2. Bickel, P. J. and Wichura, M. J. (1971). Convergence criteria for multiparameter stochastic processes and some applications. Ann. Math. Statist. 42, 1656-1670.
3. Brockwell, P. J. and Davis, R. A. (1996). Introduction to Time Series and Forecasting. Springer - Verlag, New York.
4. Chaudhuri, P. and Marron, J. S. (1999). SiZer for exploration of structures in curves. J. Amer. Statist. Assoc. 94, 807-823.
5. Chaudhuri, P. and Marron, J. S. (2000). Scale space view of curve estimation. Ann. Statist. 28, 408-428.
6. Doukhan, P. (1994). Mixing: Properties and Examples. Lecture Notes in Statistics 85. Springer, New York.
7. Durrett, R. (2005). Probability: Theory and Examples (3rd ed.). Duxbury Press, Belmont, CA.
8. Erästö, P. and Holmström, L. (2005). Bayesian multiscale smoothing for making inferences about features in scatterplots. J. Comput. Graph. Statist. 14, 569-589.
9. Fan, J. and Gijbels, I. (1996). Local Polynomial Modelling and Its Applications. Chapman & Hall, London.
10. Godtliebsen, F. and Øigård, T. A. (2005). A visual display device for significant features in complicated signals. Comput. Statist. Data Anal. 48, 317-343.
11. Hannig, J. and Lee, T. C. M. (2006). Robust SiZer for exploration of regression structures and outlier detection. J. Comput. Graph. Statist. 15, 101-117.
12. Hannig, J. and Marron, J. S. (2006). Advanced distribution theory for SiZer. J. Amer. Statist. Assoc. 101, 484-499.
13. Hsing, T., Husler, J. and Riess, R. D. (1996). The extremes of a triangular array of normal random variables. Adv. Appl. Probab. 6, 671-686.
14. Kim, C. S. and Marron, J. S. (2006). SiZer for jump detection. J. Nonparatnetr. Stat. 18, 13-20.
15. Lindeberg, T. (1994). Scale Space Theory in Computer Vision. Kluwer, Boston.
16. Øigård, T. A., Rue, H. and Godtliebsen, F. (2006). Bayesian multiscale analysis for time series data. Comput. Statist. Data Anal. 51, 1719-1730. (Pubitemid 44709238)
17. Park, C, Hernández-Campos, F., Marron, J. S. and Smith, F. D. (2005). Long-range dependence in a changing Internet traffic mix. Computer Networks 48, 401-422.
18. Park, C, Hernández Campos, F., Le, L., Marron, J. S., Park, J., Pipiras, V., Smith, F. D., Smith, R. L., Trovero, M. and Zhu, Z. (2006). Long-range dependence analysis of internet traffic. Under revision, Technometrics. Web-available at http://www.stat.uga.edu/-cpark/papers/ LRDWebPage5.pdf
19. Park, C, Godtliebsen, F., Taqqu, M., Stoev, S. and Marron, J. S. (2007a). Visualization and inference based on wavelet coefficients, SiZer and SiNos. Comput. Statist. Data Anal. 51, 5994-6012.
20. Park, C, Lazar, N. A., Ahn, J. and Sornborger, A. (2007b). Do different parts of the brain have the same dependence structure? A multiscale analysis of the temporal and spatial characteristics of resting fMRI data. Technical Repart 2007-8, Department of Statistics, University of Georgia.
21. Park, C. and Kang, K.-H. (2008). SiZer analysis for the comparison of regression curves. Comput. Statist. Data Anal. 52, 3954-3970.
22. Park, C, Marron, J. S. and Rondonotti, V. (2004). Dependent SiZer: goodness of fit tests for time series models. J. Appl. Stat. 31, 999-1017.
23. Rondonotti, V., Marron, J. S. and Park, C. (2007). SiZer for time series: a new approach to the analysis of trends. Electronic J. Statist. 1, 268-289.
24. Utev, S. A. (1990). The central limit theorem for ℓ-mixing arrays of random variables, Theory Probab. Appl., 35, 110-117.