Diagnostics For Heteroscedasticity In Linear And Partial Linear Regression Model With Missing Response Variables

Missing data is ubiquitous phenomena in practical applications.Missing data brings a lot of difficulties to statistical analysis.In statistical inference,if we ignore missing data,and just use fully observable data,the results may not in accordance with the actual conditions.Therefore,the research on dealing with missing data has practical significance.The regression model is an early developed statistical model in statistics and is one of the most widely used data analysis methods.The model evolved from a parametric regression model to a nonparametric regression model,and a semiparametric regression model in the past decades of practice and application.This paper mainly studies linear regression models and partial linear regression models.In regression models,it is generally assumed that the error terms of the model are independent of each other and have the same variance.If the model has heteroscedasticity,the results obtained from the conventional statistical inference of the model may be unreasonable,such as the parameter estimator is not effective;the significance of the variable is lost.Therefore,it is necessary to test whether the model has heteroscedasticity before statistical inference.This paper mainly studies the heteroscedasticity test of linear models and partial linear models with missing response variables.Firstly,the random missing data is complemented by the idea of regression borrowing.Secondly,the empirical likelihood method is introduced into the heteroscedasticity test of the model.We construct the empirical likelihood ratio statistic and prove that the statistic has an asymptotic chi-square distribution under the the null hypothesis.Finally,the numerical simulation is carried out by R software.The results show that our method performs well both in size and power,and proves the feasibility of the empirical likelihood method in the heteroscedasticity test.