Estimation For Single-index Varying Coefficient Model With Covariate Measurement Error

Single-index Varying Coefficient Model has the advantages of Single-index model as well as Varying Coefficient Model,and it can better fit the actual data.It is a hot spot of present research in recent years.In this article,estimation for single-index varying under measurement error data is considered,more details are as follows:In first chapter,the research status and required theoretical results of single-index varying coefficient model with covariate measurement error are presented.The second chapter studies the estimation in single-index varying coefficient EV regression model when there is only one component.We propose a new bias-corrected procedure based on the observed data and gain the consistency and asymptotic normality of unknown parameters.Finally,we test the given estimators by running a simulation.The third chapter investigates the estimation in a class of single-index varying coefficient regression model when some covariates are contaminated with measurement errors.A bias-corrected least square procedure based on the theory of the last chapter is proposed.Large sample properties of the proposed estimators are also established.More importantly,a special case is identified in which the naive procedure provides consistent estimates for the single index parameters.