基于Monte-Carlo方法的强非线性函数方差估计

Variance estimation of intensive nonlinear functions based on Monte-Carlo method

以Monte Carlo方法为基础研究了强非线性函数的方差估计问题。对直接观测量的方差进行了随机扰动 ,将由线性同余法产生的一组伪随机数用Box Muller变换法转换为服从N(0 ,1)分布的正态伪随机数 ,并对伪随机数作了多项统计检验。在此基础上应用Bessel公式统计出强非线性函数的模拟方差。算例表明 :Monte Carlo方法估计出的非线性函数的方差比经典方法估计出的方差更优。

Based on the way of Monte Carlo, the problems of variance estimation of intensive nonlinear function has been studied. By random disturbance of the standard deviation of directly observed values, a group of false random values of nonlinear function which submit to the regular distribution were produced, then they were transfered into false random value which submit to the N (0, 1) distribution by the way of Box Muller, and some statistical tests had been done on them. On the basis of these statistics, the visual variance of intensive nonlinear function was counted by Bessel formula. Example shows that the variance estimation of intensive nonlinear function counted by the way of Monte Carlo variance estimation has some advantages over that counted by the way of classical variance estimation.