Parameter Estimation Of Two Kinds Of Statistical Models Based On Laplace Distribution

Laplace distribution is an important distribution in statistics.In this paper,we study the parameter estimation of two kinds of statistical models based on Laplace distribution,more details are as follows:1.Based on a Tweedie-type formula developed under the Laplace distribution,we propose a new bias correction estimation procedure for regression parameters in a simple linear model when the measurement error follows a Laplace distribution.Large sample properties,including the consistency and the asymptotic normality of the proposed estimates,are investigated.The finite sample performance of the proposed estimates are evaluated via simulation studies,as well as comparison studies with some existing estimation procedures.2.Based on the fact that the Laplace distribution can be written as a scale mixture of a normal and a latent distribution,the idea of EM algorithm and the Least absolute estimation,we propose a robust estimation procedure for mixture linear regression models with right censored data by assuming that the error terms follow a Laplace distribution.In addition,simulations are done to demonstrate that the proposed estimators of the regression coefficients are robust and higher efficiency than traditional MLE and EM algorithm.A sensitivity study is also conducted based on a real data example to illustrate the application of the proposed method.