A nonparametric probability density estimator is proposed that is optimal with respect to a discretized form of a continuous penalized-likelihood criterion functional. Approximation results relating the discrete estimator to the estimate obtained by solving the corresponding infinite-dimensional problem are presented. The discrete estimator is shown to be consistent. The numerical implementation of this discrete estimator is outlined and examples displayed. A simulation study compares the integrated mean square error of the discrete estimator with that of the well-known kernel estimators. Asymptotic rates of convergence of the discrete estimator are also investigated.
Publié le : 1980-07-14
Classification:
G2G05,
G2E10,
Nonparametric density estimation,
maximum likelihood estimation,
kernel density estimation
@article{1176345074,
author = {Scott, D. W. and Tapia, R. A. and Thompson, J. R.},
title = {Nonparametric Probability Density Estimation by Discrete Maximum Penalized- Likelihood Criteria},
journal = {Ann. Statist.},
volume = {8},
number = {1},
year = {1980},
pages = { 820-832},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345074}
}
Scott, D. W.; Tapia, R. A.; Thompson, J. R. Nonparametric Probability Density Estimation by Discrete Maximum Penalized- Likelihood Criteria. Ann. Statist., Tome 8 (1980) no. 1, pp. 820-832. http://gdmltest.u-ga.fr/item/1176345074/