Approximation for Contaminated Distribution and Its Applications
Yang Yuanxi ①, Chai Hongzhou ②, Song Lijie ② (① Xi'an Research Institute of Surveying and Mapping, Xi'an,Shaanxi,710054) (② Zhengzhou Institute of Surveying and Mapping, Zhengzhou,Henan,450052)
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.