Bayesian methods for wavelet series in single-index models

Journal of Computational and Graphical Statistics

Volumn 14, Issue 4, 2005, Pages 770-794

  Park, Chun Gun ^a   Vannucci, Marina ^b   Hart, Jeffrey D ^b  

^a National Cancer Center   (South Korea)

^b TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Markov chain Monte Carlo; Nonequispaced design; Nonparametric regression; Wavelet shrinkage

Indexed keywords

EID: 29544432684     PISSN: 10618600     EISSN: None     Source Type: Journal    
DOI: 10.1198/106186005X79007     Document Type: Article

References (30)

1. Antoniadis, A., Bigot, J., and Sapatinas, T. (2001), "Wavelet Estimators in Nonparametric Regression: A Comparative Simulation Study," Journal of Statistical Software, 6, 1-83.
2. Antoniadis, A., Gregoire, G., McKeague, I. W. (2004), "Bayesian Estimation in Single-Index Models," Statistica Sinica, 14, 1147-1164.
3. Antoniadis, A., Gregoire, G., and Vial, P. (1997), "Random Design Wavelet Curve Smoothing," Statistics and Probability Letters, 35, 235-232.
4. Cai, T., and Brown, L. D. (1998), "Wavelet Shrinkage for Nonequispaced Samples," The Annals of Statistics, 26, 1783-1799.
5. Carlin, B. P., and Chib, S. (1995), "Bayesian Model Choice via Markov Chain Monte Carlo," Journal of the Royal Statistical Society, Series B, 57, 473-484.
6. Carroll, R. J., Fan, J., Gijbels, I., and Wand, M. P. (1997), "Generalized Partially Linear Single-Index Models," Journal of the American Statistical Association, 92, 477-489.
7. Daubechies, I. (1992), Ten Lectures on Wavelets, SIAM CBMS-NSF Conference Series, 61.
8. Donoho, D., and Johnstone, I. (1994), "Ideal Spatial Adaption via Wavelet Shrinkage," Biometrika, 81, 425-455.
9. Donoho, D., Johnstone, I., Kerkyacharian, G., and Picard, D. (1996), "Density Estimation by Wavelet Thresholding," The Annals of Statistics, 24, 508-539.
10. Gilks, W. R., Richardson, S., and Spiegelhalter, D. J. (1996), Markov Chain Monte Carlo in Practice, London: Chapman and Hall.
11. Green, P. J. (1995), "Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination," Biometrika, 82, 711-732.
12. Hall, P., and Patil, P. (1995), "Formulae for Mean Integrated Squared Error of Nonlinear Wavelet-Based Density Estimators," The Annals of Statistics, 23, 905-928.
13. Härdle, W., Hall, P., and Ichimura, H. (1993), "Optimal Smoothing in Single-Index Models," The Annals of Statistics, 21, 157-178.
14. Härdle, W., and Stoker, T. M. (1989), "Investigating Smooth Multiple Regression by the Method of Average Derivatives," Journal of the American Statistical Association, 84, 986-995.
15. Hart, J.D. (1997), Nonparametric Smoothing and Lack-of-Fit Tests, Berlin: Springer Verlag.
16. Hart, J. D., and Yi, S. (1998), "One-Sided Cross-Validation," Journal of the American Statistical Association, 93, 620-631.
17. Ichimura, H. (1993), "Semiparametric Least Squares (SLS) and Weighted SLS Estimation of Single-Index Models," Journal of Econometrics, 58, 71-120.
18. Kerkyacharian, G., and Picard, D. (1993), "Density Estimation by Kernel and Wavelet Methods: Optimality of Besov Spaces," Statistics & Probability Letters, 18, 327-336.
19. Li, K. C., and Duan, N. (1989), "Regression Analysis Under Link Violation," The Annals of Statistics, 17, 1009-1052.
20. Mallat, S. G. (1989), "A Theory for Multiresolution Signal Decomposition: the Wavelet Representation," IEEE Transactions on Pattern Analysis and Machine Intelligence, 11, 674-693.
21. Morris, J. S., Vannucci, M., Brown, P. J., and Carroll, R. J. (2003), "Wavelet-Based Nonparametric Modeling of Hierarchical Functions in Colon Carcinogenesis" (with discussion), Journal of the American Statistical Association, 98, 573-597.
22. Müller, P., and Vidakovic, B. (1999), "MCMC Methods in Wavelet Shrinkage: Non-equally Spaced Regression, Density and Spectral Density Estimation," in Bayesian Inference in Wavelet Based Models, eds. B. Vidakovic, and P. Müller, Berlin: Springer Verlag, pp. 1-18.
23. Nason, G. P. (2002), "Choice of Wavelet Smoothness, Primary Resolution and Threshold in Wavelet Shrinkage," Statistics and Computing, 12, 219-227.
24. Rao, C. R. (1973), Linear Statistical Inference and its Applications (2nd ed.), New York: Wiley.
25. Stoker, T. M. (1986), "Consistent Estimation of Scaled Coefficients," Econometrica, 54,1461-1481.
26. Vannucci, M., and Vidakovic, B. (1997), "Preventing the Dirac Disaster: Wavelet Based Density Estimation," Journal of the Italian Statistical Society, 6, 145-159.
27. Vidakovic, B., and Ruggeri, F. (2001), "BAMS Method: Theory and Simulations," Sankya, Series B, 63,234-253.
28. Walter, G. G. (1992), "Approximation of Delta Function by Wavelets," Journal of Approximation Theory, 71, 329-343.
29. Xia, Y., Tong, H., and Li, W. K. (1999), "On Extended Partially Linear Single-Index Models," Biometrika, 86, 831-842.
30. Yu, Y., and Ruppert, D. (2002), "Penalized Spline Estimation for Partially Linear Single-Index Models," Journal of the American Statistical Association, 97, 1042-1054.