The Heteroscedastical Test For A Class Of Semi-parametric Errors-in-variables Models

Semi-parametric regression models are important statistical models which can avoid the problem of curse of dimensionality and have the characteristics of high efficiency and high robustness.Those models have rich theory and wide applications in many fields,such as information science?biomedical?financial engineering?economic management?quality control?traffic engineering?energy and environment?humanities and socialsciences and other fields.Now,it has become one of the top research topics in statistics.In practical applications,we usually encounter this situation that the data cannot observed directly for some reason but contains measurement errors.In statistical research,models with measurement errors are often referred to as EV models or measurement error models.This paper focuses on the semi-parametric model of the covariate with measurement error.In regression models,we request that the residuals are independent identical distribution.Violating this assumption,we can have adverse consequences for the efficiency of estimators.Such as the invalidity of the parameter estimator and loss the significance of the variable test.This paper focuses on the heteroscedastical test of partially linear single index errors-in-variables models and the heteroscedastical test of semiparametric varying-coefficient partially linear errors-in-variables models.Firstly,under the null hypothesis,we estimate the unknown parameters and unknown functions.Secondly,we construct an empirical likelyhood ratio test and prove that the testing statistics has an asymptotic chi-square distribution.Finally,we use R to simulation our method and simulation results show that our method performs well both in size and power.