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Empirical likelihood confidence region for parameters in linear errors-in-variables models with missing data

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Abstract

The multivariate linear errors-in-variables model when the regressors are missing at random in the sense of Rubin (1976) is considered in this paper. A constrained empirical likelihood confidence region for a parameter β 0 in this model is proposed, which is constructed by combining the score function corresponding to the weighted squared orthogonal distance based on inverse probability with a constrained region of β 0. It is shown that the empirical log-likelihood ratio at the true parameter converges to the standard chi-square distribution. Simulations show that the coverage rate of the proposed confidence region is closer to the nominal level and the length of confidence interval is narrower than those of the normal approximation of inverse probability weighted adjusted least square estimator in most cases. A real example is studied and the result supports the theory and simulation’s conclusion.

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Correspondence to Hengjian Cui.

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This research is supported by the Natural Science Foundation of China under Grant Nos. 10771017 and 11071022, and Key Project of MOE, PRC under Grant No. 309007.

This paper was recommended for publication by Editor Guohua ZOU.

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Zhang, J., Cui, H. Empirical likelihood confidence region for parameters in linear errors-in-variables models with missing data. J Syst Sci Complex 24, 540–553 (2011). https://doi.org/10.1007/s11424-010-8111-z

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  • DOI: https://doi.org/10.1007/s11424-010-8111-z

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