|
Teoriya Veroyatnostei i ee Primeneniya, 1970, Volume 15, Issue 1, Pages 139–142
(Mi tvp1614)
|
|
|
|
This article is cited in 100 scientific papers (total in 100 papers)
Short Communications
Remarks on non-parametric estimates of density functions and regression curves
È. A. Nadaraya Tbilisi Ivane Javakhishvili State University
Abstract:
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.
Received: 24.04.1968
Citation:
È. A. Nadaraya, “Remarks on non-parametric estimates of density functions and regression curves”, Teor. Veroyatnost. i Primenen., 15:1 (1970), 139–142; Theory Probab. Appl., 15:1 (1970), 134–137
Linking options:
https://www.mathnet.ru/eng/tvp1614 https://www.mathnet.ru/eng/tvp/v15/i1/p139
|
Statistics & downloads: |
Abstract page: | 459 | Full-text PDF : | 223 | First page: | 1 |
|