Improvement on Some Known Nonparametric Uniformly Consistent Estimators of Derivatives of a Density
Singh, R. S.
Ann. Statist., Tome 5 (1977) no. 1, p. 394-399 / Harvested from Project Euclid
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Based on a random sample from a univariate distribution with density $f$, this note exhibits a class of kernel estimators of the $p$th order derivative $f^{(p)}$ of $f, p \geqq 0$ fixed. These estimators improve some known estimators of $f^{(p)}$ by weakening the conditions, sharpening the rates of convergence, or both for the properties of strong consistency, asymptotic unbiasedness and mean square consistency, each uniform on the real line.
Publié le : 1977-03-14
Classification:  Nonparametric estimation,  $p$th order derivative of a density,  uniform convergence,  rates,  62G05 
@article{1176343805,
     author = {Singh, R. S.},
     title = {Improvement on Some Known Nonparametric Uniformly Consistent Estimators of Derivatives of a Density},
     journal = {Ann. Statist.},
     volume = {5},
     number = {1},
     year = {1977},
     pages = { 394-399},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176343805}
}

Singh, R. S. Improvement on Some Known Nonparametric Uniformly Consistent Estimators of Derivatives of a Density. Ann. Statist., Tome 5 (1977) no. 1, pp.  394-399. http://gdmltest.u-ga.fr/item/1176343805/