Simulation-Extrapolation Estimation In Modal Regression Model With Measurement Error

Comparing to the mean and quantile regression techniques,the modal regression is more efficient and robust to outliers in the data,or when the regression error possesses a heavy-tailed distribution.Therefore,the study on modal regression has been extensively attracted by statisticians.However,the modal regression models are always contaminated with measurement errors due to various reasons.The new and effective estimation procedures need to be developed when the ordinary techniques no longer applicable.This paper studies the estimation problem for parametric modal regression model and nonparametric modal regression model with measurement error.For the parametric modal regression models,when the covariates are contaminated with normal measurement error,by means of kernel density estimation,a simulation extrapolation estimation procedure is proposed in this paper for estimating the unknown parameters.Under some suitable conditions,large sample properties of the proposed estimator,including the consistency and asymptotic normality,are thoroughly investigated.In addition,a large number of simulation studies are also conducted to examine the robustness and effectiveness performance of the proposed method.For the nonparametric modal regression models,when the covariates are contaminated with normal measurement error,by means of local linear modal regression estimation procedure,a simulation extrapolation estimation procedure is also proposed in this paper for estimating the unknown nonparametric function.The proposed estimator is shown to be asymptotically normal under some regularity conditions.Similarly,a large number of simulation studies are conducted to examine the robustness and effectiveness performance of the proposed method.