Teoriâ veroâtnostej i ee primeneniâ, Tome 15 (1970) no. 1, pp. 139-142
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È. A. Nadaraya. Remarks on non-parametric estimates of density functions and regression curves. Teoriâ veroâtnostej i ee primeneniâ, Tome 15 (1970) no. 1, pp. 139-142. http://geodesic.mathdoc.fr/item/TVP_1970_15_1_a14/
@article{TVP_1970_15_1_a14,
author = {\`E. A. Nadaraya},
title = {Remarks on non-parametric estimates of density functions and regression curves},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {139--142},
year = {1970},
volume = {15},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1970_15_1_a14/}
}
TY - JOUR
AU - È. A. Nadaraya
TI - Remarks on non-parametric estimates of density functions and regression curves
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1970
SP - 139
EP - 142
VL - 15
IS - 1
UR - http://geodesic.mathdoc.fr/item/TVP_1970_15_1_a14/
LA - ru
ID - TVP_1970_15_1_a14
ER -
%0 Journal Article
%A È. A. Nadaraya
%T Remarks on non-parametric estimates of density functions and regression curves
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1970
%P 139-142
%V 15
%N 1
%U http://geodesic.mathdoc.fr/item/TVP_1970_15_1_a14/
%G ru
%F TVP_1970_15_1_a14
In the present paper, sufficient conditions for $\sup\limits_{-\infty and $\sup\limits_{(x,y)\in\mathbf R_2}|f_n(x,y)-f(x,y)|\to0$ as $n\to\infty$ with probability 1 are found, where $\widetilde y_n(x)$ and $f_n(x,y)$ are given by (1) and (12) respectively, $y(x)$ is the regression curve of $Y$ on $X$, and $f(x,y)$ is their two-dimensional density function.
