Asymptotically Optimum Kernels for Density Estimation at a Point
Sacks, Jerome ; Ylvisaker, Donald
Ann. Statist., Tome 9 (1981) no. 1, p. 334-346 / Harvested from Project Euclid
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Kernel estimation of $f(0)$ is considered where $f$ is a density in some class $\mathscr{F}$ of $d$-dimensional densities, described in terms of a Taylor series expansion. A sequence of kernels which asymptotically minimizes the maximum mean square error of estimation over $\mathscr{F}$ is given. The shape of the kernel is fixed, the size of the window depends on $f(0)$, and an easily computed estimate is obtained to efficiently adapt the sequence to the unknown value of $f(0)$.
Publié le : 1981-03-14
Classification:  Density estimation,  mean square error,  asymptotically minimax kernel estimates,  62G20,  62G05 
@article{1176345399,
     author = {Sacks, Jerome and Ylvisaker, Donald},
     title = {Asymptotically Optimum Kernels for Density Estimation at a Point},
     journal = {Ann. Statist.},
     volume = {9},
     number = {1},
     year = {1981},
     pages = { 334-346},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176345399}
}

Sacks, Jerome; Ylvisaker, Donald. Asymptotically Optimum Kernels for Density Estimation at a Point. Ann. Statist., Tome 9 (1981) no. 1, pp.  334-346. http://gdmltest.u-ga.fr/item/1176345399/