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Discussion: Efficiency and Self‐efficiency With Multiple Imputation Inference
Author(s) -
Meng XiaoLi,
Romero Martin
Publication year - 2003
Publication title -
international statistical review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.051
H-Index - 54
eISSN - 1751-5823
pISSN - 0306-7734
DOI - 10.1111/j.1751-5823.2003.tb00215.x
Subject(s) - inefficiency , estimator , inference , imputation (statistics) , computer science , econometrics , variance (accounting) , statistics , efficiency , data mining , mathematics , missing data , artificial intelligence , machine learning , economics , microeconomics , accounting
Summary By closely examining the examples provided in Nielsen (2003), this paper further explores the relationship between self‐efficiency (Meng, 1994) and the validity of Rubin's multiple imputation (RMI) variance combining rule. The RMI variance combining rule is based on the common assumption/intuition that the efficiency of our estimators decreases when we have less data. However, there are estimation procedures that will do the opposite, that is, they can produce more efficient estimators with less data. Self‐efficiency is a theoretical formulation for excluding such procedures. When a user, typically unaware of the hidden self‐inefficiency of his choice, adopts a self‐inefficient complete‐data estimation procedure to conduct an RMI inference, the theoretical validity of his inference becomes a complex issue, as we demonstrate. We also propose a diagnostic tool for assessing potential self‐inefficiency and the bias in the RMI variance estimator, at the outset of RMI inference, by constructing a convenient proxy to the RMI point estimator.