A different perspective on the Propagation-Separation Approach

Electronic Journal of Statistics

Volumn 7, Issue 1, 2013, Pages 2702-2736

  Becker, Saskia M A ^a   Mathé, Peter ^a  

^a WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

Author keywords

Exponential families; Local likelihood; Propagation; Separation; Structural adaptive smoothing

Indexed keywords

EID: 84892393051     PISSN: 19357524     EISSN: None     Source Type: Journal    
DOI: 10.1214/13-EJS860     Document Type: Article

References (19)

1. Akkouchi, M. On the convolution of exponential distributions. J. Chung-cheong Math. Soc., 21(4):501-510, 2008.
2. Becker, S. M. A., Tabelow, K., Voss, H. U., Anwander, A., Hei-demann, R. M., and Polzehl, J. Position-orientation adaptive smoothing of diffusion weighted magnetic resonance data (POAS). Med. Im-age Anal., 16(6):1142-1155, 2012. URL http://dx.doi.org/10.1016/j. media.2012.05.007.
3. Becker, S. M. A., Tabelow, K., Mohammadi, S., Weiskopf, N., and Polzehl, J. Adaptive smoothing of multi-shell diffusion-weighted magnetic resonance data by msPOAS. Preprint no. 1809, WIAS, Berlin, 2013.
4. Belomestny, D. and Spokoiny, V. Spatial aggregation of local likelihood estimates with applications to classiffcation. Ann. Statist., 35(5):2287-2311, 2007. URL http://dx.doi.org/10.1214/ 009053607000000271. MR2363972
5. Divine, D. V., Polzehl, J., and Godtliebsen, F. A Propagation-Separation Approach to estimate the autocorrelation in a time-series. Non-linear Processes in Geophysics, 15(4):591-599, 2008.
6. Lepskiǐ, O. V. A problem of adaptive estimation in Gaussian white noise. Teor. Veroyatnost. i Primenen., 35(3):459-470, 1990. URL http://dx. doi.org/10.1137/1135065. MR1091202
7. Lepskiǐ, O. V., Mammen, E., and Spokoiny, V. Optimal spatial adaptation to inhomogeneous smoothness: an approach based on kernel estimates with variable bandwidth selectors. The Annals of Statistics, 25(3):929-947, 1997. MR1447734
8. Li, Y., Zhu, H., Shen, D., Lin, W., Gilmore, J. H., and Ibrahim, J. G. Multiscale adaptive regression models for neuroimaging data. J. R. Stat. Soc. Ser. B Stat. Methodol., 73(4):559-578, 2011. URL http://dx.doi.org/10.1111/j.1467-9868.2010.00767.x. MR2853730
9. Li, Y., Gilmor, J.H., Wang, J., Styner, M., Lin, W., and Zhu, H. Twinmarm: two-stage multiscale adaptive regression methods for twin neuroimaging data. IEEE Trans. Med. Imaging, 31(5):1100-1112, 2012. URL http://www.ncbi.nlm.nih.gov/pubmed/22287236.
10. Mathai, A. M. Storage capacity of a dam with gamma type inputs. Ann. Inst. Statist. Math., 34(3):591-597, 1982. URL http://dx.doi.org/10. 1007/BF02481056. MR0695077
11. Mathffe, P. and Pereverzev, S. V. Regularization of some linear ill-posed problems with discretized random noisy data. Math. Comp., 75(256):1913-1929 (electronic), 2006. URL http://dx.doi.org/10.1090/ S0025-5718-06-01873-4. MR2240642
12. Moschopoulos, P. G. The distribution of the sum of independent gamma random variables. Ann. Inst. Statist. Math., 37(3):541-544, 1985. URL http://dx.doi.org/10.1007/BF02481123. MR0818052
13. Polzehl, J. aws: Adaptive Weights Smoothing, 2012. URL http://cran. r-project.org/package=aws. R-package version 1.9-1.
14. Polzehl, J. and Spokoiny, V. Adaptive weights smoothing with applications to image restoration. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 62:335-354, 2000. MR1749543
15. Polzehl, J. and Spokoiny, V. Propagation-Separation Approach for local likelihood estimation. Probability Theory and Related Fields, 135:335-362, 2006. MR2240690
16. Polzehl, J. and Spokoiny, V. Structural Adaptive Smoothing by Propagation-Separation Methods. In Handbook of Data Visualization, Springer Handbooks Comp. Statistics, pages 471-492, Springer Berlin Heidelberg, 2008.
17. Polzehl, J., Voss, H.U., and Tabelow, K. Structural adaptive segmentation for statistical parametric mapping. NeuroImage, 52:515-523, 2010.
18. Spokoiny, V. and Vial, C. Parameter tuning in pointwise adaptation using a propagation approach. Ann. Statist., 37(5B):2783-2807, 2009. MR2541447
19. Tabelow, K., Polzehl, J., Spokoiny, V., and Voss, H. U. Diffusion tensor imaging: structural adaptive smoothing. Neuroimage, 39:1763-1773, 2008.