污染分布的逼近及应用

污染分布是抗差估计的基础。本文试图从观测值残差入手，首先逼近各观测值方差，进而由方差的变化逼近污染正态分布密度。逼近的基本思想是：将异常观测值的方差扩大。文中构造了方差膨胀函数。基于方差膨胀的污染正态分布，可由最小二乘估计获得模型参数的抗差估计解；并由方差传播定律及Ｂａｙｅｓ推断理论解算参数的验后方差－协方差及置信区间。文中给出了一个算例。

Approximation for Contaminated Distribution and Its Applications

A contaminated normal density is numerically approached by a variance variant normal distribution in which the variation of the variance of an observation is based on the observational residual. The variances correspond to the outlying observations which are generally too optimistic will be amplified. An effective amplification function for inflating the variance of the outlying observation is constructed, that provides the way to make up the effects of outlying observations. The Least Squares estimation based on the new approached density can result the robust estimates of model parameters. The posterior covariance matrices and the confidence regions of the parameter estimates are readily obtained by the well known error propagation law and Bayesian inference based on the approached density. A numerical example shows that the approaching density is effective in robustness and in efficiency.