摘要
In this paper,we mainly study how to estimate the error density in the ultrahigh dimensional sparse additive model,where the number of variables is larger than the sample size.First,a smoothing method based on B-splines is applied to the estimation of regression functions.Second,an improved two-stage refitted crossvalidation(RCV)procedure by random splitting technique is used to obtain the residuals of the model,and then the residual-based kernel method is applied to estimate the error density function.Under suitable sparse conditions,the large sample properties of the estimator,including the weak and strong consistency,as well as normality and the law of the iterated logarithm,are obtained.Especially,the relationship between the sparsity and the convergence rate of the kernel density estimator is given.The methodology is illustrated by simulations and a real data example,which suggests that the proposed method performs well.
基金
supported by National Natural Science Foundation of China (Grant Nos. 11971324 and 11471223)
Interdisciplinary Construction of Bioinformatics and Statistics
Academy for Multidisciplinary Studies, Capital Normal University
