非参数回归模型样条估计量的分布

Distribution of Spline Estimators for Nonparametric Regression Models

为探究非参数回归模型中非参数函数估计量的分布,本文在标准正态误差情形下首先得到了均值函数样条估计量的正态分布,然后得到了方差函数基于残差的样条估计量的渐近分布,并采用单个卡方变量线性函数来近似方差函数估计量的渐近分布。通过数值模拟验证了均值函数估计量的分布和方差函数估计量的渐近分布。

To explore the distribution of nonparametric function estimator in the nonparametric regression model, we first obtain the normal distribution of the spline estimator of the mean function in the standard normal error casein this paper. Then the asymptotic distribution of the spline estimator of the variance function based on the residuals is obtained. And the linear function of individual chi-square variable is used to approximate the asymptotic distribution of the variance function es-timator. The distribution of the mean function estimator and the asymptotic distribution of the variance function estimator are illustrated by numerical simulations.