Spatial aggregation of local likelihood estimates with applications to classification

Annals of Statistics

Volumn 35, Issue 5, 2007, Pages 2287-2311

  Belomestny, Denis ^a   Spokoiny, Vladimir ^a  

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

Author keywords

Adaptive weights; Classification; Exponential family; Local likelihood

Indexed keywords

EID: 50449086446     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053607000000271     Document Type: Article

References (18)

1. BELOMESTNY, D. and SPOKOINY, V. (2006). Spatial aggregation of local likelihood estimates with applications to classification. SFB 649 Discussion Paper 2006-036.
2. BREIMAN, L. (1996). Stacked regressions. Machine Learning 24 49-64.
3. CAI, Z., FAN, J. and LI, R. (2000). Efficient estimation and inference for varying-coefficient models. J. Amer. Statist. Assoc. 95 888-902.
4. CATONI, O. (2004). Statistical Learning Theory and Stochastic Optimization. Lecture Notes in Math. 1851. Springer, Berlin.
5. FAN, J., FARMEN, M. and GIJBELS, I. (1998). Local maximum likelihood estimation and inference. J. R. Stat. Soc. Ser. B Stat. Methodol. 60 591-608.
6. FAN, J. and ZHANG, W. (1999). Statistical estimation in varying coefficient models. Ann. Statist. 27 1491-1518.
7. JUDITSKY, A. and NEMIROVSKI, A. (2000). Functional aggregation for nonparametric estimation. Ann. Statist. 28 681-712.
8. LEPSKI, O., MAMMEN, E. and SPOKOINY, V. (1997). Optimal spatial adaptation to inhomogeneous smoothness: An approach based on kernel estimates with variable bandwidth selectors. Ann. Statist. 25 929-947.
9. LEPSKI, O. and SPOKOINY, V. (1997). Optimal pointwise adaptive methods in nonparametric estimation. Ann. Statist. 25 2512-2546.
10. LI, J. and BARRON, A. (1999).Mixture density estimation. In Advances in Neural Inforamtion Processing Systems 12 (S. A. Sola, T. K. Leen and K. R. Müller, eds.). Morgan Kaufmann Publishers, San Mateo, CA.
11. LOADER, C. R. (1996). Local likelihood density estimation. Ann. Statist. 24 1602-1618.
12. POLZEHL, J. and SPOKOINY, V. (2006). Propagation-separation approach for local likelihood estimation. Probab. Theory Related Fields 135 335-362.
13. RIGOLLET, PH . and TSYBAKOV, A. (2005). Linear and convex aggregation of density estimators. Manuscript.
14. SPOKOINY, V. (1998). Estimation of a function with discontinuities via local polynomial fit with an adaptive window choice. Ann. Statist. 26 1356-1378.
15. STANISWALIS, J. G. (1989). The kernel estimate of a regression function in likelihood-based models. J. Amer. Statist. Assoc. 84 276-283.
16. TIBSHIRANI, R. and HASTIE, T. J. (1987). Local likelihood estimation. Amer. Statist. Assoc. 82 559-567.
17. TSYBAKOV, A. (2003). Optimal rates of aggregation. In Computational Learning Theory and Kernel Machines (B. Scholkopf and M. Warmuth, eds.) 303-313. Lecture Notes in Artificial Intelligence 2777. Springer, Heidelberg.
18. YANG, Y. (2004). Aggregating regression procedures to improve performance. Bernoulli 10 25-47.