Robust Estimation Based On Laplace Distribution

Developing various robust estimation methods has become a hot research topic in statistics. Classical estimation methods usually assume that the observed values obey a certain distribution. For example, when we deal with the financial data, the probability distribution of the yield is usually normally distributed. In the practice, the yield has a leptokurtosis and fat-tail distribution. The assumption of normality is not reasonable, and it will make a serious distortion of results when using least squares estimation. Compared with normal distribution, Laplace distribution has peak fat-tail characteristic, we find that when the observed values of the linear model obey the Laplace distribution, using LAD estimation can get a relatively satisfactory result.This dissertation mainly introduces the robust linear regression via Laplace distribution. The LAD estimation of the general linear regression is introduced firstly. Secondly, the LAD estimation of EIV linear regression is discussed. The LAD estimation of mixed EIV linear regression is researched at last.In the second chapter, I introduce the characters of Laplace distribution. In chapter 3, I introduce the LAD estimation of the general linear regression. The main idea is that the parameters estimators are obtained by the Newton-Raphson iterative programs, the core is to design the EM algorithm. On the basic of this argument, the LAD estimation of EIV linear regression and LAD estimation of mixture EIV linear regression are introduced. The article mainly carries on the numerical simulation research about EIV linear regression models. I use matlab compiler to design the programs to prove that LAD estimation is very effective.