Estimation And Application Of Varying-coefficient Partially Linear Errors-in-variables Model

With the continuous development of science and technology,various models capable of processing large amounts of data are constantly proposed,and their processing technology has been rapidly developed-The varying-coefficient partially linear errors-in-variables model combines the advantages of the variable coefficient model and the errors-in-variables model,which not only solves the problem of dimension disaster of the non-parametric model,but also keeps the good adaptability of the variable coefficient model.At the same time,considering the existence of measurement errors in model variables,the model of error variables is studied to make the estimation and results more accurate.This paper studies the varying-coefficient partially linear errors-in-variables model.In view of the serious complex collinearity between model covariables,a ridge estimation of the model is proposed on the basis of profile least squares estimation method.The ridge estimation expressions of constant coefficient and variable coefficient are obtained,and the asymptotic properties of the estimation results are studied.Based on the given assumptions,we prove the asymptotic normality of the parameter,and give the concrete form of the asymptotic normal distribution to be followed.By comparing the method of profile least-squares estimation with that of ridge estimation through numerical simulation experiments,it is verified that the ridge estimation result of the model is better than that of the model when the complex collinearity of covariates is serious.Finally,the paper makes a practical analysis of the air quality in Harbin,.In order to study the influence of heating,straw burning,temperature,humidity and wind level on the air quality index,we establish the varying-coefficient partially linear models with and without measurement errors,and use the profile least squares estimation and ridge estimation methods to estimate the model.Different models are compared and the estimated results are analyzed.The results show that the estimation result of the model with measurement errors is better than that of the model without measurement error,and the ridge estimation method should be used when the complex collinearity is seriousHeating,straw burning and humidity are positively correlated with air quality index,while wind level is negatively correlated with air quality index.And the influence of temperature on air quality index is weak.The air quality index is decreasing year by year,and the heating period index is obviously higher than the non-heating period.