Statistical Inference For Varying-coefficient Partially Nonlinear Models With Multiplicative Distortion Measurement Errors

With the advent of the era of big data,the form and structure of the data are becoming more and more complex.In statistical decision-making,neither simple linear regression models or nonparametric models can not explain the relationship between the response and the covariates exactly,and make an accurate trend prediction of the interested variables.Then,semi-parametric models have received extensive attention from scholars at home and abroad.In biology,medicine,finance and other fields,the data are observed with measurement errors due to some subjective and objective reasons.When we deal with the measurement error data,the native procedure by simply ignoring measurement errors always leads to a large deviation between the estimates and true vales,which results in wrong decisions.In actual situation,we must take the data with measurement errors into consideration when building statistical models.In this case,we can obtain relatively superior inference results.Therefore,we discuss the statistical inference problem of the varying-coefficient partially nonlinear model where the variables are observed with multiplicative distortion measurement errors.In this thesis,we investigate the estimation and inference for the varying-coefficient partially nonlinear model where the response and the covariates in partially nonlinear part can not be directly observed,but are distorted in a multiplicative fashion by unknown distorting functions of a commonly observable confounding variable.Firstly,we adopt the nonparametric regression to estimate the unobservable variables,which we call the calibration estimation procedure.Based on the calibrated variables,we introduce the estimates of the parameter vector and the coefficient function vector in the measurement errors model.Secondly,we propose a generalized likelihood ratio(GLR)test to check whether or not the varying coefficient is a constant vector or not.Finally,simulation studies are conducted to verify the validity of the proposed corrected profile nonlinear estimation and GLR test.Boston housing price data is analyzed for an illustration of our proposed procedure.