Weighted Local Linear Estimation Of Regression Function With Random Deletion Index

The estimation of nonparametric regression function is a hot issue in mathematical statistics.Most of the statistical methods used in the past are based on complete data,but in the actual statistical processing,missing data and deleted data are inevitable.In practical application,due to various reasons,the dependent variable T can't be completely observed due to right deletion,and it is more common for some deletion indicators to be randomly missing.Therefore,the processing of this kind of complex data is very important.In this paper,three weighted local linear estimation methods of nonparametric regression function are proposed,namely calibration,interpolation and inverse probability,based on the data with random missing index deletion and in the case of multi-dimensional covariates(d ?1),using the weighted method,and the asymptotic normality of these three estimation methods is studied.First,we construct the estimation of nonparametric regression function of covariates.The weighted local linear estimator and NW estimator of multivariate nonparametric regression function under three data cases(complete data,right deletion and random deletion index)are introduced respectively.Under the condition of random deletion index,three weighted local linear estimators,namely calibration,interpolation and inverse probability of multivariate nonparametric regression function,are constructed respectively,and two solutions of these estimators are derived.Then,the asymptotic normality theorems of the three weighted local linear estimation methods of multivariate nonparametric regression function calibration,interpolation and inverse probability are given.At the same time,an important advantage of the weighted local linear estimator is given: the boundary point effect,that is,compared with the NW estimator,the weighted local linear estimator can automatically adjust the boundary point estimator.Then,three weighted local linear estimation methods are simulated and applied in practice.The weighted local linear estimation method proposed in this paper was applied to the clinical data of primary biliary cholangitis patients by numerical simulation of two nonparametric regression functions with one and two dimensional covariables.The results show that the weighted local linear estimation method of multivariate nonparametric regression function constructed in this paper is better than the kernel estimation.Finally,the asymptotic normality theorems of calibration,interpolation and inverse probability weighted local linear estimation methods are theoretically proved.The research content and main research results of this paper are summarized,and the research results of this paper have certain theoretical and practical significance.