Statistical Inference Of The Transformation Model Under Missing Data

With the advent of the era of big data and the emergence of mass data,the problem of missing data is becoming more and more serious.The missing data brings great trouble to applied research and statistical analysis.Traditional statistical analysis methods cannot be directly applied to the processing of missing data.Improper processing of missing data will lead to wrong conclusions.Therefore,the processing of missing data has always been a frontier and hot issue in statistics.In this paper,the statistical inference problem of the transformation model under the absence of data is considered.We use the inverse probability weighted smooth maximum rank correlation estimation method to estimate the parameters of interest in the transformation model.The consistency and asymptotic normality of the proposed estimates are proved.Numerical simulation and data analysis show that the proposed method performs very well.This paper is divided into six chapters.The first chapter mainly introduces the research background,significance and research status at home and abroad.We introduce in detail the causes,missing patterns,missing mechanisms and corresponding processing methods of data loss,and describe the basic idea of Inverse probability weighted and the estimation principle of Maximized rank correlation,in chapter 2.In chapter 3,the inverse probability weighted smooth maximum rank correlation estimation method is proposed,and the consistency and asymptotic normality of the proposed estimation are given.The method proposed in this paper involves the tendency score function,which is set as a parameter model.In chapter 4,we evaluate the finite sample properties of the proposed estimates by numerical simulation.In this chapter,we first set up the missing mechanism of data,and then carried out numerical simulation for linear model,logarithmic conversion model and box-cox conversion model,and compared the estimated effect with Complete case analysis.The sensitivity of the proposed estimation method to window width h was tested by setting different window width h.In chapter 5,the method proposed in this paper is applied to the financial statement data containing missing data,and the comparison with the estimated results of CC method shows that the proposed IPWSMRC method is more effective and robust.