Statistical Inference For Linear Regression Models With Contaminated Data

Statistical analysis problems about contaminated data often occur in practical occasions just as censored data. Davis [1] firstly proposed the concepts of contami-nated data and contaminated coefficient in 1952. The so-called contaminated model is the model that the distributions of its observations or at least part of them are un-known, and that is caused by the interference of contaminated sources which come from contaminated data (we assume that the distributions of these data are known) but are different from the model. Zheng Zukang et al.[2] proposed the regression model about two different kinds of contaminated data in 1996, and estimated the parameters and contaminated coefficient via LS method under the assumption that the regres-sion errors, as well as contaminated sources, are normally distributed. In 1998, Chen Minghua[3] estimated the parameters and contaminated coefficient via the least square method without the condition of normal distribution, and proved strong consistency of these estimators.In this paper, our main work is divided into two parts. Firstly, considering linear regression model of contaminated data, LAD estimators of the regression parameters are presented under the assumption that regression errors and contaminated sources obey Laplace distribution. And the corresponding consistency and asymptotic nor-mality are proved. The small-sample properties of the estimation method are also analyzed by related simulations. From this, we show that our method performs well in smaller case. Then, the confidence interval of the regression parameter is given by using least absolutely deviation and the empirical likelihood method.