The Research Of Estimation Method On Semiparametric Model With Measurement Errors

In recent years, semiparametric varying-coefficient partially linear model is a newdevelopment direction of high-dimensional data in regression analysis, so the researchon semiparametric model is not only of great theoretical value, but also of practicalsignificance. Linear model, partially linear model and varying-coefficient model are alldegradation forms of semiparametric varying-coefficient partially linear model. Invarying-coefficient partially linear models, because a few regression coefficients arenonparametric functions of some factors, they have reduced the model deviationsubstantially and avoided the curse of dimensionality. The model has characteristic ofbeing interpreted in linear model, and it also has robustness, flexibility of nonparametricmodels and other features, which make the model not only can be used to analyseindependent data, but also longitudinal data and time series data effectively, so it hasbeen used widely in practice.In application of semiparametric models, measurement error may appear becauseof some instruments and environmental factors. If we build regression model withignoring measurement error directly, it will lead to big deviation in regression ananlysisresult, and then we come to unreasonable conclusion. Hence, many statisticians hasbegun to study measurement error models deeply and replaced the traditional regressionmodels gradually, which makes measurement error model be widely used in economics,epidemiology, engineering and other fields.This paper mainly discusses the estimated method of varying-coefficient partiallylinear regression model. In the case that the random error is conditionallyheteroskedastic, we can obtain a semiparametrically efficient estimator of parametricpart by general series estimation method. While in practical application, the covariatesare always measured with errors. If we ignore the measurement error, the general seriesestimator above would be biased. In the paper, we put forward correctional generalseries estimation method, by this way, consistency and asymptotic normality ofparametric estimator are investigated. Meanwhile, we discussed convergence rate ofestimator in nonparametric part. Finally，some simulation studies are proposed to verifythe good effect of the modified estimation, which is superior to the estimator without modification through general series method.