Parameter Estimation Of Quantile Regression Model Of Pollution Data

In actual study and work,some pollution data are often encountered,like censored data and truncated data,and pollution data is a kind of incomplete data.For the linear regression model of pollution data(or pollution data model),many scholars often use least square method or least absolute deviation method to estimate the parameters,and prove the consistency and asymptotic normality of parameter estimators.But the least squares robustness is poor,and it also satisfies normality,homogeneity and other assumptions.The least absolute deviation to a certain extent is better than the least square,but it can only reflect the change of the median of the dependent variable with the covariate,and only a regression line can be obtained.The inequality of the income that we are interested in,the unequal wealth of the wealth,the unreasonable distribution of the resources,if the previous method is still adopted,not only can not reflect the essence of the fact,but also ignore the important information.Therefore,it is very important to apply quantile regression to the pollution data model.Quantile regression is not only robust,but also can get multiple fitting lines according to work needs,which has greater research value for model analysis.There are three main aspects of this work: first,the linear regression model of contaminated data is reviewed.The least squares and least absolute deviation are used to estimate the parameters of the linear regression model of contaminated data.The two is to introduce the concept of quantile and quantile function,and the pollution data and subdivision.In combination with multiple regression models,the quantile regression model of pollution data is proposed.Under the condition that the variance caused by the system is greater than the variance caused by pollution,the quantile regression is used to estimate the parameters of the model,and the consistency and asymptotic normality of the estimator are proved to the pollution data of the inequality problem.The theory provides the theoretical basis;three is to modify the third kind of pollution data model,that is,the known time pollution model,give the correct parameter estimation,and apply this model to the Laplace distribution,also give the estimation of the parameters,and find that whether it is normal distribution or Laplace distribution,as long as it satisfies one.For a generalized third class of models,the same parameter estimation can be obtained.