Consistent Cross-Validated Density Estimation
Chow, Y.-S. ; Geman, S. ; Wu, L.-D.
Ann. Statist., Tome 11 (1983) no. 1, p. 25-38 / Harvested from Project Euclid
Application of nonparametric density estimators generally requires the specification of a "smoothing parameter." The kernel estimator, for example, is not fully defined until a window width, or scaling, for the kernels has been chosen. Many "data-driven" techniques have been suggested for the practical choice of smoothing parameter. Of these, the most widely studied is the method of cross-validation. Our own simulations, as well as those of many other investigators, indicate that cross-validated smoothing can be an extremely effective practical solution. However, many of the most basic properties of cross-validated estimators are unknown. Indeed, recent results show that cross-validated estimators can fail even to be consistent for seemingly well-behaved problems. In this paper we will review the application of cross-validation to the smoothing problem, and establish $L_1$ consistency for certain cross-validated kernels and histograms.
Publié le : 1983-03-14
Classification:  Cross-validation,  consistency,  nonparametric density estimation,  62G05,  62A10
@article{1176346053,
     author = {Chow, Y.-S. and Geman, S. and Wu, L.-D.},
     title = {Consistent Cross-Validated Density Estimation},
     journal = {Ann. Statist.},
     volume = {11},
     number = {1},
     year = {1983},
     pages = { 25-38},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176346053}
}
Chow, Y.-S.; Geman, S.; Wu, L.-D. Consistent Cross-Validated Density Estimation. Ann. Statist., Tome 11 (1983) no. 1, pp.  25-38. http://gdmltest.u-ga.fr/item/1176346053/