Remarks on non-parametric estimates of density functions and regression curves

È. A. Nadaraya

Teoriâ veroâtnostej i ee primeneniâ, Tome 15 (1970) no. 1, pp. 139-142

Résumé

In the present paper, sufficient conditions for $\sup\limits_{-\infty<a\le x\le b<\infty}|\widetilde y_n(x)-y(x)|\to0$ 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.