Remarks on Non-Parametric Estimates for Density Functions and Regression Curves
Remarks on Non-Parametric Estimates for Density Functions and Regression Curves
复制标题
关于密度函数和回归曲线的非参数估计的备注
DOI：
10.1137/1115015
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发表时间：
1970
影响因子：
0.6
通讯作者：
E. Nadaraya
中科院分区：
文献类型：
--
作者：
E. Nadaraya
设（xl, yl） （x2, Y2），“”，(x。， y.)是密度函数为f （X, y）的二维随机变量（X, y）的n个独立观测值的样本。表示随机变量X的密度函数乘以f (X)和Y关于X的回归曲线乘以Y (X)“Y (X) yf (ylx) dy”。下面我们假设f (X)和Y (X)在整条实线上是连续的。本文给出了[1]-[3]中回归曲线和二维密度估计在C中几乎肯定分别收敛于理论y (x)和f （x, y）的充分条件。
Let (xl, yl),(x2, Y2),"",(x., y.) be a sample of n independent observations of a two-dimensional random variable (X, Y) with density function f (x, y). Denote the density function of the random variable X byf (x) and the regression curve of Y with respect to X by y (x)" y (x) yf (ylx) dy.In the following we shall assume thatf (x) and y (x) are continuous over the entire real line. This note gives sufficient conditions for the estimates for the regression curve and twodimensional density, found in [1]-[3], to converge almost surely in C to the theoretical y (x) and f (x, y), respectively.