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Empirical likelihood for response differences in two linear regression models with missing data

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Abstract

Consider two linear models X i = U′ i β + ε i Y j = V′ j γ + η j with response variables missing at random. In this paper, we assume that X, Y are missing at random (MAR) and use the inverse probability weighted imputation to produce ‘complete’ data sets for X and Y. Based on these data sets, we construct an empirical likelihood (EL) statistic for the difference of X and Y (denoted as Δ), and show that the EL statistic has the limiting distribution of χ 21 , which is used to construct a confidence interval for Δ. Results of a simulation study on the finite sample performance of EL-based confidence intervals on Δ are reported.

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Authors and Affiliations

  1. Department of Mathematics, Guangxi Normal University Guilin, Guilin, 541004, China

    Yong-song Qin, Tao Qiu & Qing-zhu Lei

Authors
  1. Yong-song Qin
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  2. Tao Qiu
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  3. Qing-zhu Lei
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Corresponding author

Correspondence to Yong-song Qin.

Additional information

Supported by the National Natural Science Foundation of China (No. 11271088, 11361011, 11201088) and Natural Science Foundation of Guangxi (No. 2013GXNSFAA(019004 and 019007), 2013GXNSFBA019001).

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Qin, Ys., Qiu, T. & Lei, Qz. Empirical likelihood for response differences in two linear regression models with missing data. Acta Math. Appl. Sin. Engl. Ser. 31, 963–976 (2015). https://doi.org/10.1007/s10255-015-0516-y

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  • DOI: https://doi.org/10.1007/s10255-015-0516-y

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