Multivariate small area estimation under nonignorable nonresponse

作     者：Danny Pfeffermann Michael Sverchkov 

作者机构：National Statistician and CBS DirectorJerusalemIsrael Department of StatisticsHebrew UniversityJerusalemIsrael Southampton Statistical Sciences Research Institute(S3RI)University of SouthamptonSouthamptonUK Bureau of Labor StatisticsWashingtonDCUSA 

出 版 物：《Statistical Theory and Related Fields》 (统计理论及其应用（英文）)

年 卷 期：2019年第3卷第2期

页      面：213-223页

学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 070101[理学-基础数学] 

主　　题：Distribution of missing data imputation under nonignorable nonresponse missing information principle MSE estimation NMAR nonresponse 

摘      要：We consider multivariate small area estimation under nonignorable, not missing at random(NMAR) nonresponse. We assume a response model that accounts for the different patterns ofthe observed outcomes, (which values are observed and which ones are missing), and estimatethe response probabilities by application of the Missing Information Principle (MIP). By this principle, we first derive the likelihood score equations for the case where the missing outcomes areactually observed, and then integrate out the unobserved outcomes from the score equationswith respect to the distribution holding for the missing data. The latter distribution is definedby the distribution fitted to the observed data for the respondents and the response model. Theintegrated score equations are then solved with respect to the unknown parameters indexingthe response model. Once the response probabilities have been estimated, we impute the missing outcomes from their appropriate distribution, yielding a complete data set with no missingvalues, which is used for predicting the target area means. A parametric bootstrap procedure isdeveloped for assessing the mean squared errors (MSE) of the resulting predictors. We illustratethe approach by a small simulation study.