Geodesic
On the integral mean squared error of some non-parametric estimates of the probability density
Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 1, pp. 131-139 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is shown that in estimating the density $p(x)$ by means of the statistics (1) the sequence $\tau_n=\tau_n^0$ is optimal in the sense of the minimum integral mean squared error $U_n^2(\tau_n)$. An estimate $\widehat\tau_n=\widehat\tau_n(X_1, X_2,\dots,X_n)$ for $\tau_n^0$ is constructed and a theorem is proved that gives conditions under which $U_n^2(\widehat\tau_n)\sim U_n^2(\tau_n^0)$. 
@article{TVP_1974_19_1_a9,
     author = {\`E. A. Nadaraya},
     title = {On the integral mean squared error of some non-parametric estimates of the probability density},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {131--139},
     year = {1974},
     volume = {19},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1974_19_1_a9/}
}
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È. A. Nadaraya. On the integral mean squared error of some non-parametric estimates of the probability density. Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 1, pp. 131-139. http://geodesic.mathdoc.fr/item/TVP_1974_19_1_a9/