Penalized partially linear models using sparse representations with an application to fMRI time series

IEEE Transactions on Signal Processing

Volumn 53, Issue 9, 2005, Pages 3436-3448

  Fadili, Jalal M ^a   Bullmore, Ed ^b  

^a Centre National de la Recherche Scientifique   (France)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

fMRI; Neuroimaging; Partially linear models; Penalized estimation; Sparse representations; Wavelets

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; ESTIMATION; MATHEMATICAL MODELS; NEUROPHYSIOLOGY; TIME SERIES ANALYSIS; WAVELET TRANSFORMS;

FUNCTIONAL MAGNETIC RESONANCE IMAGING; NEUROIMAGING; PARTIALLY LINEAR MODELS; PENALIZED ESTIMATION; SPARSE REPRESENTATIONS;

MAGNETIC RESONANCE IMAGING;

EID: 27644549681     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2005.853207     Document Type: Article

References (41)

1. W. Härdle, H. Liang, and J. Gao, Partially Linear Models. New York: Springer-Verlag, 2000.
2. T. Hastie and T. Tibshirani, Generalized Additive Models. London, U.K.: Chapman and Hall, 1990.
3. N. E. Heckman, "Spline smoothing in partly linear models," J. R. Statist. Soc. B, vol. 48, pp. 244-248, 1986.
4. R. L. Eubank and P. Whitney, "Convergence rates for estimation in certain partially linear models," J. Statist. Planning Inference, vol. 23, pp. 33-43, 1989.
5. R. L. Eubank and P. Speckman, "Curve fitting by polinomial-trigonometric regression," Biometrika, vol. 77, pp. 1-9, 1990.
6. R. L. Eubank and J. D. Hart, "Testing the goodness-of-fit in regression via order selection criteria," J. Amer Statist. Assoc., vol. 85, pp. 387-392, 1990.
7. R. L. Eubank, E. L. Kambour, J. T. Kim, K. Klipple, C. S. Reese, and M. Schimek, "Estimation in partially linear models," Comput. Statist. Data Anal., vol. 29, pp. 27-34, 1998.
8. H. Chen, "Convergence rates for parametric components in a partly linear model," Ann. Statist., vol. 16, pp. 136-146, 1988.
9. P. Speckman, "Kernel smoothing in partial linear models," J. R. Statist. Soc. B, vol. 50, pp. 413-436, 1988.
10. J. T. Gao, "Large Sample Theory in Semiparametric Regression Models," Ph.D. dissertation, Graduate School, Univ. Sci. Technol. China, Hefei, China, 1992.
11. T. A. Severini and J. G. Staniswalis, "Quasilikelihood estimation in semiparametric models," J. Amer. Statist. Assoc., vol. 89, pp. 501-511, 1994.
12. R. J. Carroll, J. Fan, I. Gijbels, and M. P. Wand, "Generalized partially single-index models," J. Amer. Statist. Assoc., vol. 92, pp. 477-489, 1997.
13. J. Rice, "Convergence rates for partially splined models," Statist. Probab. Lett., vol. 4, pp. 203-208, 1986.
14. W. Härdle and P. Vieu, "Kernel regression smoothing of time series," J. Time Series Anal., vol. 13, pp. 209-232, 1992.
15. P. K. Bhattacharya and P. L. Zhao, "Semiparametric inference in a partial linear model," Ann. Statist., vol. 25, pp. 244-262, 1997.
16. X. W. Chang and L. Qu, "Wavelet estimation of partially linear models," Comput. Statist. Data Anal., vol. 47, pp. 31-48, 2004.
17. F. G. Meyer, "Wavelet based estimation of a semi parametric generalized linear model of fMRI time-series," IEEE Trans. Med. Imag., vol. 22, no. 3, pp. 315-322, Mar. 2003.
18. B. Ardekani, J. Kershaw, K. Kashikura, and I. Kanno, "Activation detection in functional MRI using subspace modeling and maximum likelihood estimation," IEEE Trans. Med. Imag., vol. 18, no. 2, pp. 101-114, Feb. 1999.
19. S. Sardy, A. Bruce, and P. Tseng, "Block coordinate relaxation methods for nonparametric wavelet denoising," J. Comput. Graphical Statist., vol. 9, no. 2, pp. 361-379, 2000.
20. J. M. Fadili and E. T. Bullmore, "Wavelet-generalised least squares: A new BLU estimator of linear regression models with 1/f errors," NeroImag., vol. 15, pp. 217-232, 2002.
21. M. J. Fadili and E. T. Bullmore, "Semiparametric time series regression using library of orthonormal waveform bases and the MDL principle," ENSI de Caen, Caen, France, GREYC CNRS UMR 6072, 2001.
22. S. Sardy and P. Tseng, "Amlet, ramlet, and gamlet: Automatic nonlinear fitting of additive models, robust and generalized, with wavelets," J. Comput. Graphical Statist., vol. 13, no. 2, pp. 283-373 099, 2000.
23. M. Nikolova, "Local strong homogeneity of a regularized estimator," SIAM J. Appl. Math., vol. 61, no. 2, pp. 633-658, 2000.
24. R. Gribonval, R. M. Figueras, and P. Vandergheynst, "A simple test to check the optimality of a sparse signal approximation," IRISA, Rennes, France, 2004.
25. A. Antoniadis and J. Fan, "Regularization of wavelets approximations," J. Amer. Statist. Assoc., vol. 96, no. 455, pp. 939-963, 2001.
26. P. Clarke, "Optimization and nonsmooth analysis," in Classic Appl. Math. SIAM, Second ed. Philadelphia, PA, 1990.
27. U. Amato and D. T. Vuza, "Wavelet approximation of a function from samples affected by noise," Revue Roumaine Math. Pures Appl., vol. 42, pp. 481-493, 1997.
28. Y. Meyer, Ondelettes et Opérateurs. Paris, France: Hermann, 1992.
29. 2 norms with application to Bayesian estimation," IEEE Trans. Signal Process., vol. 42, no. 3, pp. 618-627, Mar. 1994.
30. D. L. Donoho and I. M. Johnstone, "Ideal spatial adaptation via wavelet shrinkage," Biometrika, vol. 81, pp. 425-455, 1994.
31. P. Craven and G. Wahba, "Smoothing noisy data with spline functions," Numer. Math, vol. 31, pp. 377-403, 1979.
32. M. Jansen, M. Malfait, and A. Bultheel, "Generalized cross validation for wavelet thresholding," Signal Process., vol. 56, no. 1, pp. 33-44, 1997.
33. T. W. Anderson, An Introduction to Multivariate Statistical Analysis, Second ed. New York: Wiley, 1984.
34. M. Durban, C. Hackett, and I. Currie, "Approximate standards errors in semiparametric models," Biometrics, vol. 55, pp. 699-703, 1999.
35. A. Buja, T. J. Hastie, and R. J. Tibshirani, "Linear smoothers and additive models (with discussion)," Ann. Statist., vol. 17, no. 2, pp. 453-555, 1989.
36. W. Härdle, S. Huet, E. Mammen, and S. Sperlich, "Bootstrap inference in semiparametric generalized additive models," Econ. Th., vol. 20, 2004, to be published.
37. B. Efron and R. J. Tibshirani, "An introduction to the bootstrap," in Monographs on Statistics and Applied Probability. New York: Chapman and Hall, 1993.
38. S. Chen, D. L. Donoho, and M. Saunders, "Atomic decomposition by basis pursuit," SIAM J. Scientific Comput., vol. 20, pp. 33-61, 1998.
39. J.-L. Starck, M. Elad, and D. L. Donoho, "Image decomposition via the combination of sparse representations and variational approach," IEEE Trans. Image Process., to be published.
40. H. H.-S. Lu, S.-Y. Huang, and F.-J. Lin, "Generalized cross-validation for wavelet shrinkage in nonparametric mixed effects models," J. Comput. Graphical Statist., vol. 12, no. 3, pp. 714-730, 2003.
41. R. A. Horn and C. R. Johnson, Matrix Analysis. New York: Camridge Univ. Press, 1997.