Semiparametric double robust and efficient estimation for mean functionals with response missing at random

Xu Guo, Yun Fang, Xuehu Zhu, Wangli Xu, Lixing Zhu

Research output: Contribution to journalArticle

Abstract

Under dimension reduction structure, several semiparametric estimators for the mean of missing response are proposed, which can efficiently deal with the dimensionality problem. Specifically, a generalized version of Augmented Inverse Probability Weighting estimator (AIPW) is proposed and its double robustness, estimation consistency and asymptotic efficiency are investigated. A generalized version of Inverse Probability Weighting (IPW) estimator is also introduced. An asymptotic efficiency reduction phenomenon occurs in the sense that the IPW estimator with the true selection probability is asymptotically less efficient than the one with an estimated selection probability. Besides, two partial imputation and two complete imputation estimators are discussed. We further systematically investigate the comparisons among these estimators in theory. Several simulation studies and a real data analysis are conducted for performance examination and illustration.

Original languageEnglish (US)
Pages (from-to)325-339
Number of pages15
JournalComputational Statistics and Data Analysis
Volume128
DOIs
StatePublished - Dec 1 2018

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Missing at Random
Efficient Estimation
Robust Estimation
Inverse Probability Weighting
Estimator
Asymptotic Efficiency
Imputation
Double Robustness
Dimension Reduction
Dimensionality
Data analysis
Simulation Study
Partial

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

Cite this

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title = "Semiparametric double robust and efficient estimation for mean functionals with response missing at random",
abstract = "Under dimension reduction structure, several semiparametric estimators for the mean of missing response are proposed, which can efficiently deal with the dimensionality problem. Specifically, a generalized version of Augmented Inverse Probability Weighting estimator (AIPW) is proposed and its double robustness, estimation consistency and asymptotic efficiency are investigated. A generalized version of Inverse Probability Weighting (IPW) estimator is also introduced. An asymptotic efficiency reduction phenomenon occurs in the sense that the IPW estimator with the true selection probability is asymptotically less efficient than the one with an estimated selection probability. Besides, two partial imputation and two complete imputation estimators are discussed. We further systematically investigate the comparisons among these estimators in theory. Several simulation studies and a real data analysis are conducted for performance examination and illustration.",
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Semiparametric double robust and efficient estimation for mean functionals with response missing at random. / Guo, Xu; Fang, Yun; Zhu, Xuehu; Xu, Wangli; Zhu, Lixing.

In: Computational Statistics and Data Analysis, Vol. 128, 01.12.2018, p. 325-339.

Research output: Contribution to journalArticle

TY - JOUR

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AU - Fang, Yun

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AU - Xu, Wangli

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