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Semiparametric maximum likelihood estimation with data missing not at random
Author(s) -
Morikawa Kosuke,
Kim Jae Kwang,
Kano Yutaka
Publication year - 2017
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.11340
Subject(s) - estimator , missing data , parametric statistics , nonparametric statistics , statistical inference , semiparametric model , econometrics , inference , outcome (game theory) , parametric model , statistics , computer science , maximum likelihood , estimation , mathematics , artificial intelligence , economics , management , mathematical economics
Abstract Nonresponse is frequently encountered in empirical studies. When the response mechanism is missing not at random (MNAR) statistical inference using the observed data is quite challenging. Handling MNAR data often requires two model assumptions: one for the outcome and the other for the response propensity. Correctly specifying these two model assumptions is challenging and difficult to verify from the responses obtained. In this article we propose a semiparametric maximum likelihood method for MNAR data in the sense that a parametric assumption is used for the response propensity part of the model and a nonparametric model is used for the outcome part. The resulting analysis is more robust than the fully parametric approach. Some asymptotic properties of our estimators are derived. Results from a simulation study are also presented. The Canadian Journal of Statistics 45: 393–409; 2017 © 2017 Statistical Society of Canada