Heteroscedasticity Test For Semiparametric EV Model With Missing Response Variable

In data analysis,the ideal situation is that the collected data is perfect and valid,and there are no outliers and missing values.However,in reality,missing data and measurement error data are often generated for some reasons.In the academic world,models with measurement errors in variables are usually called EV models;for missing data,some scholars have proposed a variety of processing methods,and regression interpolation is commonly used.If missing data and measurement errors are ignored in statistical inference,it will lead to a series of problems.Therefore,before making statistical inferences,how to correctly handle missing data and measurement error data becomes very important.As a kind of regression model,semi-parametric model combines parametric and non-parametric models,so semi-parametric models have become a powerful tool for data analysis.At the same time,part of the linear model and part of the linear single-index model,as classic semi-parametric regression models,have attracted the attention of a large number of scholars.This article adds measurement error data on this basis,and further studies a partially linear EV model and a partially linear single-index EV model.When using regression models for statistical inference,it is necessary to test whether the model's random error terms have heteroscedasticity.If the random error terms in the model are independent of each other and have the same variance,it means that there is no heteroscedasticity.This article will perform heteroscedasticity testing based on empirical likelihood theory.Empirical likelihood is a statistical inference method proposed by Owen,which has some advantages that conventional statistical methods do not have.This paper mainly discusses the problem of heteroscedasticity testing for partially linear EV models and partially linear single-index EV models with missing response variables.First,the completely observed data is used to estimate the unknown parameters and smooth functions in the model.Based on this,the missing data is complemented by the idea of regression borrowing.Secondly,the idea of empirical likelihood is introduced,statistics are constructed and heteroscedasticity tests are performed on these two models respectively.Thirdly,using R language for numerical simulation,the finite sample properties of the test under different missing probabilities are studied.Then,for the partially linear EV model,the actual data is used to further illustrate that it is feasible to perform the heteroscedasticity test using the method proposed in the article.Finally,the asymptotic distribution of empirical likelihood ratio statistics based on a partially linear EV model and a partially linear single-index EV model is demonstrated.