Diagnostic Measures for Functional Linear Model with Nonignorable Missing Responses  

作　　者：Yujian Zhu Puying Zhao 

机构地区：[1]Key Lab of Statistical Modeling and Data Analysis of Yunnan Province,Yunnan University,Kunming,People’s Republic of China

出　　处：《Communications in Mathematics and Statistics》2024年第3期543-562,共20页数学与统计通讯（英文）

基　　金：supported by the General Project of National Natural Science Foundation of China(Grant No.12071416).

摘　　要：Assessing the influence of individual observations of the functional linear models is important and challenging,especially when the observations are subject to missingness.In this paper,we introduce three case-deletion diagnostic measures to identify influential observations in functional linear models when the covariate is functional and observations on the scalar response are subject to nonignorable missingness.The nonignorable missing data mechanism is modeled via an exponential tilting semiparametric functional model.A semiparametric imputation procedure is developed to mitigate the effects of missing data.Valid estimations of the functional coefficients are based on functional principal components analysis using the imputed dataset.A smoothed bootstrap samplingmethod is introduced to estimate the diagnostic probability for each proposed diagnostic measure,which is helpful to unveil which observations have the larger influence on estimation and prediction.Simulation studies and a real data example are conducted to illustrate the finite performance of the proposed methods.

关 键 词：Case deletion Diagnostic measure Functional linear model Nonignorable nonresponse Semiparametric imputation 

分 类 号：O17[理学—数学]