Testing For Heteroscedasticity In Semi-parametric Models

With the development of the economic, using only Cross-sectional data or financialtime series is not enough to solve the economic and social problem, so longitudinal datacome up at time. Since1968, longitudinal data was first introduced to the word, lots ofeconomist and statist began to research the longitudinal data. At present, longitudinal datahas become one of the hottest topics in economic and statist.In this paper, we mainly investigate the test for heteroscedasticity in partial linearmodels of longitudinal data and semi-parametric varying coefficient partially linearerrors-in-variables model.Partial linear models of longitudinal data and semi-parametricvarying coefficient partially linear errors-in-variables model are two importantsemi-parametric statistic models. They can be used at many filed, such as economicstatistics, analysis of financial time series and biomedical, they have many merit, first,Semi-parametric statistic models can effectively avoid the “dimension disaster” problem ofthe nonparametric model. Second, it contains many parametric, nonparametric andSemi-parametric models, such that the model’s explanation ability can be enhanced. So itis significant to study these two models.Since these two models were first put forward, many academicians were attracted toresearch them. However they all focus on the estimate methods and their asymptoticproperties of these two models, they seldom studied the testing heteroscedasticity. For afitted model, we request the fitted residuals are independent and homoscedasticity. If thehomoscedasticity was destroyed, that is heteroscedasticity, and this may lead to manyproblems, such as the estimate of the variance of the estimator isn’t consistent and theestimate isn’t consistent some times. Based on these considerations, this paper we mainlyfocus on the testing heteroscedasticity of these two models.This paper, we cite the empirical likelihood ratio test statistics method to these twomodels. We established empirical likelihood ratio test estimator, Under some normalconditions, we prove the chi-square distribution of the test function, that is a nonparametricversion of Wilk’s theorem. Simulation results show that our testing method does well inboth Size and Power.At last, we applied semi-parametric varying coefficient partially linear model intopractical problem. We established an accurate relationship between wheat yield and allkinds of the indicators of yield by using Semi-parametric varying-coefficient partiallinear model, which can improve the yield.