Research On The Correction Method Of Median Difference Estimation And Its Applicatio

Currently,the continuous progress of science and technology has driven the flourishing development of various fields in society.This rapid progress is due to the continuous updating of production methods,the optimization of solutions,and the precise implementation of various friendly policies.In order to make better decisions,relevant departments need to conduct a lot of research experiments and comparative analysis before implementing a series of measures,comparing the impact of different policies and measures on society,and providing strong theoretical support for decisionmaking.This thesis aims to study the correction and estimation method of the median difference in response variables between different schemes under the background of treatment effect analysis.Chapter 1 systematically introduces the research background and significance of this paper.Through the introduction of the research progress on methods of treatment effect analysis both domestically and abroad,the current research status of missing data analysis methods,non-parametric correction methods,robust treatment effect analysis methods,etc.are reviewed.The main research content and innovative points of this paper are briefly summarized.Chapter 2 reviews the classic theoretical models and methods for analyzing treatment effect problems,including traditional parameter model regression estimation methods,inverse probability weighting estimation methods,augmented inverse probability weighting estimation methods,and empirical likelihood correction estimation methods.Chapter 3 investigates the problem of median difference estimation for treatment effects of different schemes under high-dimensional data features.A quantile estimation method based on convex programming solutions for high-dimensional missing data is introduced.By constructing a special missing scenario under the analysis of the treatment effect,a convex programming-based median difference correction estimation method is proposed for high-dimensional treatment effect analysis.On this basis,by constructing the constraints of the empirical likelihood objective function,the highdimensional convex programming solution method was combined with the empirical likelihood correction method to weaken the restrictions of the model parameter assumptions,and a median difference bias correction estimation method based on convex programming solution and empirical likelihood correction was proposed.Through numerical simulations from multiple perspectives such as sample size,data dimension,error distribution,and model differences,the excellent performance of the proposed correction estimation method is demonstrated.Chapter 4 investigates the vocational education and training data from New South Wales in 1978 and the data on different drug regimens for treating AIDS.By using various methods for comparing treatment effects and comparing them with the convex programming correction estimation method proposed in this paper and the correction estimation method combined with empirical likelihood,the comparative relationships between different schemes in the two case studies are explored in detail,thus guiding practice.In addition,through case analysis,it is demonstrated that the proposed method has certain advantages over other estimation methods.Chapter 5 provides a detailed summary of the research content of this thesis and reflects on prospects for future directions and improvements based on the research results of this thesis.