Estimation For Semiparametric Varying-coefficient Partially Nonlinear Model With Missing Response At Random

Semi-parametric varying coefficient partially nonlinear models are one of the most important models in semi-parametric regression models.The model contains both parametric and non-parametric components.Therefore,the model not only has the the characteristics of easy to explain of the non-parametric model,but also has the good adaptability of the varying-coefficient model.Theoretically speaking,to deal with the semi-parametric regression model,we need to combine the common methods of the parameter regression and the non-parametric methods,but it is not a simple superposition of the two.In real life,there are many uncontrollable factors in the process of collecting data samples,causing data loss or failure to collect the accurate information.Therefore,the concept of missing data was born.The existence of missing data brings many difficulties for statistical analysis.And the phenomenon of missing data is universal.Therefore,the research of missing data in recent years has become one of the hot issues in data analysis.In this paper,we mainly study the parameter estimation in the semi-parametric varying coefficient partially nonlinear model with missing response at random.First of all,in the second chapter,we propose to use B-splines combined with profile least squares method to estimate the parameters in the varying coefficient partially nonlinear model under complete data.Then,We prove the convergence of the obtained results under appropriate conditions.In the third chapter,the paper proposes to estimate the unknown parameters in the model by combining the linear approximation method with the spline estimation equations for varying coefficient partially nonlinear models with missing response at random.Then we use the interpolation method to deal with the missing data,and use the iterative method to obtain the estimates of the parametric and non-parametric components.After that,the article also proves the convergence property of the estimators which obtained by the estimation method,under appropriate assumptions.At the end of this chapter,two simulations were conducted to testing the procedures and assess the performance of the proposed estimating.The results show that the two procedures perform well in finite samples.In the fourth chapter,this paper uses the real data to analyze and give evidences to the estimation methods proposed in the article.