A note on penalized minimum distance estimation in nonparametric regression

Canadian Journal of Statistics

Volumn 31, Issue 3, 2003, Pages 267-274

  Bunea, Florentina ^a   Wegkamp, Marten H ^a  

^a FLORIDA STATE UNIVERSITY   (United States)

Author keywords

Complexity penalty; L1 risk; Minimum distance estimators; Model selection; Nonparametric regression; Shatter coefficient

Indexed keywords

EID: 0742306054     PISSN: 03195724     EISSN: None     Source Type: Journal    
DOI: 10.2307/3316086     Document Type: Article

References (12)

1. M. Anthony & P. L. Bartlett (1999). Neural Network Learning: Theoretical Foundations. Cambridge University Press.
2. G. Biau & L. Devroye (2002a). Density estimation by the penalized combinatorial method. Unpublished manuscript.
3. G. Biau & L. Devroye (2002b). A note on density model size testing. Unpublished manuscript.
4. L. Devroye, L. Györfi & G. Lugosi (1996). A Probabilistic Theory of Pattern Recognition. Springer-Verlag, New York.
5. L. Devroye & G. Lugosi (1996). A universally acceptable smoothing factor for kernel density estimation. The Annals of Statistics, 24, 2499-2512.
6. L. Devroye & G. Lugosi (1997). Nonasymptotic smoothing factors, kernel complexity and Yatracos classes. The Annals of Statistics, 25, 2626-2637.
7. L. Devroye & G. Lugosi (2000). Combinatorial Methods in Density Estimation. Springer-Verlag, New York.
8. L. Györfi, M. Kohler, A. Krzyżak & H. Walk (2002). A Distribution-Free Theory of Nonparametric Regression. Springer-Verlag, New York.
9. N. W. Hengartner and M. H. Wegkamp (2001). Estimation and selection procedures in regression: an L1 approach. The Canadian Journal of Statistics, 29, 621-632.
10. T. Nicoleris & Y. G. Yatracos (1997). Rates of convergence of estimates, Kolmogorov's entropy and the dimensionality reduction principle in regression. The Annals of Statistics, 25, 2493-2511.
11. M. H. Wegkamp (1999). Quasi-universal bandwidth selection for kernel density estimators. The Canadian Journal of Statistics, 27, 409-420.
12. Y. G. Yatracos (1985). Rates of convergence of minimum distance estimators and Kolmogorov entropy. The Annals of Statistics, 13, 768-774.