Semiparametric Inference For Expectile Regression In The Semi-supervised Learning Framework

How to maximize the use of data is a issue that has been concerned about since the development of statistics,however,the proposal of the concept of semi-supervision learning has brought the gospel to the solution of this problem.Objectively speaking,the original data to be analyzed by statistical scholars in reality is not only large but also messy,especially the lack of data,which makes the data analysis work,for example,the fitting model,falling into a deadlock.In addition,in most cases,the proportion of lack of samples in the total sample is much higher than the complete sample,which shows that if the part of the lack of data is abandoned,then there will be a lot of information lost carried by this part of the data.As a result,the final statistical analysis results will differ greatly from the actual situation.This article divides the complete data and missing data into labeled datasets and unlabeled datasets,respectively.The purpose is to derive a semi-supervised estimator that are more effective than the supervision estimator.The expectile model,which can reflect the error more sensitively than the quantile model,is adopted in this paper,so it can enhance the grasp of the information loss rate to a certain extent.In this paper,parameter interpolation method is adopted to reduce dimension,iterative weighted least squares method is used to drive estimation convergence,nonlinear least squares estimation is used to select bandwidth,and other measures are taken to solve the problems of dimension disaster,data divergence,kernel function and bandwidth selection,so that the semi-supervised estimatior proposed in this paper can maximize the use of the information carried by the total sample,and obtain the benchmark estimator based on the loss function of labeled data using semi-supervised estimator as the medium.Finally,using Nadaraya-Wattson regression to synthesize the information of labeled data and unlabeled data to derivea semi-supervised estimator.Combined with various outcome indicators,numerical simulation experiments show that compared with the benchmark estimation,semi-supervised estimation is more stable in the estimation and has less difference from the true value of the parameter,especially in the incorrectly set model,which is more applicable.