Geodesic
Generalized kernel density estimator
Teoriâ veroâtnostej i ee primeneniâ, Tome 44 (1999) no. 3, pp. 634-645

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We introduce a new class of nonparametric density estimators. It includes the classical kernel density estimator as well as the popular Abramson's estimator. We show that generalized estimators may perform much better than the classical one if the distribution has a heavy tail. The asymptotics of the mean squared error (MSE), optimal (in a sense) kernel, and smoothing parameter are found.
Keywords: kernel density estimation, square lose function, optimal smoothing parameter.
Mots-clés : optimal kernel 
@article{TVP_1999_44_3_a8,
     author = {S. Yu. Novak},
     title = {Generalized kernel density estimator},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {634--645},
     publisher = {mathdoc},
     volume = {44},
     number = {3},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1999_44_3_a8/}
}
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S. Yu. Novak. Generalized kernel density estimator. Teoriâ veroâtnostej i ee primeneniâ, Tome 44 (1999) no. 3, pp. 634-645. http://geodesic.mathdoc.fr/item/TVP_1999_44_3_a8/