Diagnostics For Heteroscedasticity In Semi-parametric Varying-coefficient Partially Linear Model With Missing Response Variables Based On Empirical Likelihood

We will find that data missing is often in actual data when we are statistically modeling real-life data.There are many reasons for missing data,such as data not being collected during data collection,and data loss due to improper data storage,etc.Although many data in life are generated quickly and at low cost,and there is no impact on research,usually we delete the missing data and then research.However,the loss of data that takes huge manpower,material resources,financial resources,or a long time to observe will be a huge loss.At this time,the missing data must be completed first and then researched.The semi-parametric regression model is an important type of regression model in statistical modeling.This type of regression model is based on a linear regression model with a nonlinear regression model part.Therefore,the semi-parametric regression model not only has the interpretability of a linear regression model,but also has the robustness of a nonlinear regression model.Varying-coefficient models and vary-coefficient partially linear models are an important class of regression models.Such regression models have been widely used in economics,finance,meteorology,industry,agriculture and other fields.It is essential to test whether the residuals of the regression model have the same variance when we build the regression model.If the established regression model has heteroscedasticity,the model will not be able to predict.This paper studies Empirical likelihood based diagnostics for heteroscedasticity in semi-parametric varying-coefficient partially linear models with missing responses.In my work,I first studied the missing data completion of the varying-coefficient model and the vary-coefficient partial linear model with missing values of response variable.For the vary-coefficient model with missing response variables,we select data without missing data,use local linear regression methods to estimate the unknown function in the variable coefficient model,and bring the estimated function into the variable coefficient model.Methods complete missing data.For the partially linear variable coefficient model with missing response variables,we select data without missing response variables and use profile least squares to estimate the unknown parameters and unknown functions in the varying-coefficient partially linear model,and bring the estimated parameters and functions into In some linear variable coefficient models,the missing response variable is also completed using regression borrowing.Next,we re-estimate the unknown parameters or unknown functions for the completed data;and use empirical likelihood to diagnostics for heteroscedasticity for the vary-coefficient model and the varying-coefficient partially linear model,respectively.Then use numerical simulation to simulate the method proposed in this paper,and the simulation shows the following results.Under the null hypothesis;when there is no missing,the larger the sample size,the closer the size is to the significance level;when the sample size is constant,the smaller the missing rate,the smaller the size.Finally,relevant proofs are given.