Abstract
We extend the mean empirical likelihood inference for response mean with data missing at random. The empirical likelihood ratio confidence regions are poor when the response is missing at random, especially when the covariate is high-dimensional and the sample size is small. Hence, we develop three bias-corrected mean empirical likelihood approaches to obtain efficient inference for response mean. As to three bias-corrected estimating equations, we get a new set by producing a pairwise-mean dataset. The method can increase the size of the sample for estimation and reduce the impact of the dimensional curse. Consistency and asymptotic normality of the maximum mean empirical likelihood estimators are established. The finite sample performance of the proposed estimators is presented through simulation, and an application to the Boston Housing dataset is shown.
Highlights
Means that missing data of Y is only related to (Yo, X) and has nothing to do with Ym
Empirical likelihood [1, 2] which is widely used for nonparametric and semiparametric statistical inferences is a competitive and powerful method for constructing confidence intervals (CIs). e empirical log-likelihood ratio (ELR) usually has an asymptotic chi-squared distribution, and the CI based on EL has many excellent properties, as proposed by Owen [3]
The bias-corrected EL method was constructed via the inverse propensity weighting (IPW), mean imputation (MI), and augmented inverse propensity weighting (AIPW)
Summary
We will compare the MEL with OEL for response mean with data missing at random. For the one-dimensional covariate model, the estimating equation g(X, θ) is equal to the estimating equation φli(Yi, μ). For the multivariate covariate model, we compare the performance for different π(Xi), correlation structures, and the size of the sample
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