Propagation-separation approach for local likelihood estimation

Probability Theory and Related Fields

Volumn 135, Issue 3, 2006, Pages 335-362

  Polzehl, Jörg ^a   Spokoiny, Vladimir ^a  

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

Author keywords

Adaptive weights; Classification; Density estimation; Exponential family; Local likelihood; Propagation; Separation

Indexed keywords

EID: 33646008274     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-005-0464-1     Document Type: Article

References (28)

1. Bickel, P.J., Klaassen, C.A.J., Ritov, Y., Wellner, J.A.: Efficient and Adaptive Estimation for Semiparametric Models. Springer, 1998
2. Cai, Z., Fan, J., Li, R.: Efficient estimation and inference for varying coefficients models. J. Amer. Statist. Ass., 95, 888-902 (2000)
3. Cai, Z., Fan, J., Yao, Q.: Functional-coefficient regression models for nonlinear time series. J. Amer. Statist. Ass. 95, 941-956 (2000)
4. Fan, J., Farmen, M., Gijbels, I.: Local maximum likelihood estimation and Inference. J. Royal Statist. Soc. Ser. B, 60, 591-608 (1998)
5. Fan, J., Gijbels, I.: Data-driven bandwidth selection in local polynomial fitting: variable bandwidth and spatial adaptation. J. Royal Statist. Soc. B 57, 371-394 (1995)
6. Fan, J., Gijbels, I.: Local polynomial modelling and its applications. Chapman & Hall, London, 1996
7. Fan, J., Marron, J.S.: Fast implementations of nonparametric curve estimators. J. Comp. Graph. Statist. 3, 35-56 (1994)
8. Fan, J., Zhang, C., Zhang, J.: Generalized likelihood ratio statistics and Wilks phenomenon. Ann. Statist. 29, 153-193 (2001)
9. Fan, J., Zhang, J.: Sieve empirical likelihood ratio tests for nonparametric functions. Ann. Statist. 32, 1858-1907 (2004)
10. Friedman, J.H.: Greedy function approximation: A gradient boosting machine. Ann. Statist. 29(5), 11891232 (2001)
11. Grama, I., Polzehl, J. Spokoiny, V.: Adaptive estimation for varying coefficient generalized linear models. Manuscript in preparation 2003
12. Hastie, T.J., Tibshirani, R.J.: Varying-coefficient models (with discussion). J. Royal Statist. Soc. Ser. B 55, 757-796 (1993)
13. Hastie, T.J., Tibshirani, R.J., Friedman, J.: hThe Elements of Statistical Learning. Springer, 2001
14. Korostelev, A., Tsybakov, A.: Minimax Theory of Image Reconstruction. Springer Verlag, New York-Heidelberg-Berlin, 1993
15. Lepski, O., Mammen, E., Spokoiny, V.: Ideal spatial adaptation to inhomogeneous smoothness: an approach based on kernel estimates with variable bandwidth selection. Annals of Statistics 25 (3), 929-947 (1997)
16. Loader, C.R.: Local likelihood density estimation. Academic Press 1996
17. Müller, H.: Change-points in nonparametric regression analysis. Ann. Statist. 20, 737-761 (1992)
18. Müller, H.G., Song, K.S.: Maximum estimation of multidimensional boundaries. J. Multivariate Anal. 50 (2), 265-281 (1994)
19. Polzehl, J., Spokoiny, V.: Adaptive weights smoothing with applications to image segmentation. J. of Royal Stat. Soc. 62, Series B, 335-354 (2000)
20. Polzehl, J., Spokoiny, V.: Local likelihood modeling by adaptive weights smoothing. WIAS-Preprint No. 787, 2002
21. Polzehl, J., Spokoiny, V.: Image denoising: pointwise adaptive approach. Annals of Statistics 31, 30-57 (2003)
22. Polzehl, J., Spokoiny, V., Stǎricǎ, C.: When did the 2001 recession really end? WIAS-Preprint No. 934, 2004
23. Polzehl, J., Spokoiny, V.: Varying coefficient GARCH versus local constant volatility modeling. Comparison of the predictive power. WIAS-Preprint No. 977, 2004
24. Polzehl, J., Spokoiny, V.: Spatially adaptive regression estimation: Propagation-separation approach. WIAS-Preprin No. 998, 2004c
25. Qiu, P.: Discontinuous regression surface fitting. Ann. Statist. 26 (6), 2218-2245 (1998)
26. Spokoiny, V.: Estimation of a function with discontinuities via local polynomial fit with an adaptive window choice. Ann. Statist. 26 (4), 1356-1378 (1998)
27. Staniswalis, J.C.: The kernel estimate of a regression function in likelihood-based models. Journal of the American Statistical Association 84, 276-283 (1989)
28. Tibshirani, J.R., Hastie, T.J.: Local likelihood estimation. Journal of the American Statistical Association 82, 559-567 (1987)