局部线性回归的核函数分析

Kernel Function Analysis for Local Linear Regression

摘要: 非参数回归方法有很多，最常用的是局部多项式回归，局部线性回归是局部多项式回归的特例，局部线性回归较好的克服了边界的偏差，且有良好的渐近性质和收敛速度，因此运用较为广泛。本文采用局部线性回归方法，研究不同核函数和样本量对积分均方偏差、积分方差和积分均方误差的影响，首先研究在不同核函数下，绘制用局部线性回归方法得到的拟合值和真实值的图像，然后研究在不同核函数和样本量下，使用局部线性回归方法对积分均方偏差、积分方差和积分均方误差的影响。

Abstract: There are many nonparametric regression methods, the most commonly used is local polynomial regression, local linear regression is a special case of local polynomial regression. Local linear re-gression better overcomes the bias of the boundaries, and has good asymptotic properties and convergence speed, so it is more widely used. In this paper, we use the local linear regression method to study the effect of different kernel functions and sample sizes on the integral mean-square deviation, integral variance and integral mean-square error. Firstly, we study to plot the images of the fitted values and the true values obtained by using the local linear regression method with different kernel functions. Then we study to study the effect of the use of the local linear regression method on the integral mean-square deviation, integral variance and integral mean-square error with different kernel functions and sample sizes.