Constrained Estimation And Penalized Empirical Likelihood For Semiparametric Variable Coefficient Partially Linear EV Models

The semi-parametric variable coefficient partial linear model is a major type of semiparametric regression model.It not only retains the advantages of easy interpretation of the parametric model,but also contains non-parametric vectors with broad adaptability.Its appearance has been extremely affected by the statistical community.Inordinate attention,has still been widely valued and researched,and has been widely used in the fields of industry,agriculture,economy,medicine and finance.In the study of some practical problems,the data can not be properly observed for some reasons.However,it contains measurement errors.Such problems are usually encountered especially in the fields of biomedicine,econometrics,and agricultural production.Therefore,the research on the statistical inference of semi-parametric variable coefficient partial linear models with measurement errors is the current Hot topics in the field of statistics and has a certain theoretical significance and practical value.In practical problems,sometimes we can obtain prior information about regression parameters,and using this information will increase the efficiency of statistical inference to some extent.For example,in linear regression,when the prior information is given in a linear form,constrained least squares estimation is more effective than ordinary least squares estimation.Variable selection is commonly used in practical problems.For instance,in the fields of finance and risk management,in order to resist the impact of market fluctuations,it is often necessary to choose some based on historical data intervention with important financial indicators.This paper mainly considers the statistical inferences for semi-parametric varyingcoefficient partially linear models with measurement errors in both the parametric and the nonparametric parts.First,under the condition that the parameters have linear constraints,the asymptotic properties of the estimators and tests of unknown parameters and nonparametric functions are considered.Second,based on the penalized empirical likelihood method,the parameter estimation,variable selection,and hypothesis test of the semiparametric varying-coefficient partial linear model are discussed.The paper is divided into three chapters,and the main contents are as follows:The first chapter mainly explains the research background of this paper,introduces the model and research method of this paper in detail,and finally summarizes the main work of this paper.The second chapter studies the parameter estimation and hypothesis test of the semiparametric varying-coefficient partially linear measurement error model.When some additional linear restrictions on the parametric component are available,using the local linear regression technique?the correction for attenuation and the modified profile least squares method,the estimators of unknown parameters and nonparametric function and its asymptotic properties are discussed.Also,the problem of hypothesis testing on linear constraints is considered.Finally,the properties of the proposed method are illustrated by simulated data.The third chapter studies the penalized empirical likelihood of the semi-parametric varying-coefficient partial linear measurement error model.Firstly,based on the unbiased auxiliary function,the log-likelihood of the penalized empirical function is constructed,and it is proved that the penalized empirical likelihood has Oracle property.Secondly,the problem of hypothesis testing on parameters is considered,and the test statistics and its asymptotic distribution are given.Finally,the finite sample properties of the proposed method are verified by some simulations and a real data example.