On the Exact Asymptotic Behavior of Estimators of a Density and its Derivatives
Singh, R. S.
Ann. Statist., Tome 9 (1981) no. 1, p. 453-456 / Harvested from Project Euclid
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For an integer $p \geq 0$, Singh has proposed a class of kernel estimators $\hat{f}^{(p)}$ of the $p$th order derivative $f^{(p)}$ of a density $f$. This paper examines the detailed asymptotic behavior of these estimators. In particular, asymptotically equivalent expressions for the bias $(E\hat{f}^{(p)} - f^{(p)})$, the mean squared error $E(\hat{f}^{(p)} - f^{(p)})^2$ and the error $(\hat{f}^{(p)} - f^{(p)})$ are obtained, which in turn give exact rates of convergence of these terms to zero.
Publié le : 1981-03-14
Classification:  Exact asymptotic behavior,  density function,  derivatives of a density,  exact rate of convergence,  62G05 
@article{1176345413,
     author = {Singh, R. S.},
     title = {On the Exact Asymptotic Behavior of Estimators of a Density and its Derivatives},
     journal = {Ann. Statist.},
     volume = {9},
     number = {1},
     year = {1981},
     pages = { 453-456},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176345413}
}

Singh, R. S. On the Exact Asymptotic Behavior of Estimators of a Density and its Derivatives. Ann. Statist., Tome 9 (1981) no. 1, pp.  453-456. http://gdmltest.u-ga.fr/item/1176345413/