Smoothing Spline ANOVA for Time-Dependent Spectral Analysis

Journal of the American Statistical Association

Volumn 98, Issue 463, 2003, Pages 643-652

  Guo, Wensheng ^a   Dai, Ming ^a   Ombao, Hernando C ^b   Von Sachs, Rainer ^c  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^c UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

Locally stationary process; Smooth localized complex exponential basis; Smoothing spline; Spectral estimation; Tensor product; Time series

Indexed keywords

EID: 0242595638     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/016214503000000549     Document Type: Article

References (21)

1. Adak, S. (1998), "Time-Dependent Spectral Analysis of Non-Stationary Time Series," Journal of the American Statistical Association, 93, 1488-1501.
2. Aronszajn, N. (1950), "Theory of Reproducing Kernels," Transactions of the American Mathematical Society, 68, 337-404.
3. Dahlhaus, R. (1997), "Fitting Time Series Models to Nonstationary Processes," The Annals of Statistics, 25, 1-37.
4. Fan, J., and Kreutzberger, E. (1998), "Automatic Local Smoothing for Spectral Density Estimation," Scandinavian Journal of Statistics, 25, 359-369.
5. Gu, C., and Wahba, G. (1993a), "Semiparametric Analysis of Variance With Tensor Product Thin Plate Splines," Journal of the Royal Statistical Society, Ser. B, 55, 353-368.
6. _ (1993b), "Smoothing Spline ANOVA With Component-Wise Bayesian Confidence Intervals," Journal of Computational and Graphical statistics, 2, 97-117.
7. Guo, W. (2002), "Inference in Smoothing Spline ANOVA," Journal of the Royal Statistical Society, Ser. B, 64, 887-898.
8. Lin, Y. (2000), "Tensor Product Space ANOVA Models," The Annals of Statistics, 28, 734-755.
9. Neumann, M. H., and von Sachs, R. (1997), "Wavelet Thresholding in Anisotropie Function Classes and Application to Adaptive Estimation of Evolutionary Spectra," The Annals of Statistics, 25, 38-76.
10. Nychka, D. (1988), "Bayesian Confidence Intervals for Smoothing Splines," Journal of the American Statistical Association, 83, 1134-1143.
11. Ombao, H., Raz, J., von Sachs, R., and Malow, B. (2001), "Automatic Statistical Analysis of Bivariate Nonstationary Time Series," Journal of the American Statistical Association, 96, 543-560.
12. Ombao, H., Raz, J., von Sachs, R., and Guo, W. (2002), "The SLEX Model of a Nonstationary Time Series," Annals of the Institute of Statisical Mathematics, 54, 171-200.
13. Pawitan, Y., and O'Sullivan, F. (1994), "Nonpametric Spectral Density Estimation Using Penalized Whittle Likelihood," Journal of the American Statistical Association, 89, 600-610.
14. Priestley, M. B. (1965), "Evolutionary Spectral and Non-Stationary Process," Journal of the Royal Statistical Society, Ser. B, 28, 228-240.
15. Self, S. G., and Liang, K. Y. (1987), "Asymptotic Properties of Maximum Likelihood Estimators and Likelihood Ratio Tests Under Nonstandard Conditions," Journal of the American Statistical Association, 82, 605-610.
16. Wahba, G. (1980), "Automatic Smoothing of the Log Periodogram, " Journal of the American Statistical Association, 75, 122-132.
17. _ (1983), "Bayesian 'Confidence Intervals' for the Cross-Validated Smoothing Spline," Journal of the Royal Statistical Society, Ser. B, 45, 133-150.
18. _ (1990), Spline Models for Observational Data (CBMS-NSF Regional Conference Series in Applied Mathematics), Philadelphia: SIAM.
19. Wahba, G., Wang, Y., Gu, C., Klein, R., and Klein, B. (1995), "Smoothing Spline ANOVA for Exponential Families, With Application to the Wisconsin Epidemiological Study of Diabetic Retinopathy," The Annals of Statistics, 23, 1865-1895.
20. Whittle, P. (1962), "Gaussian Estimation in Stationary Time Series," Bulletin of the International Statistical Institute, 39, 105-129.
21. Wickerhauser, M. (1994), Adapted Wavelet Analysis From Theory to Software, Wellesley, MA: IEEE Press.