Empirical likelihood for mixed-effects error-in-variables model |
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Authors: | Qiu-hua Chen Ping-shou Zhong Heng-jian Cui |
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Affiliation: | [1]Mathematical & Physical Science School, North China Electric Power University, Beijing 102206, China [2]Department of Statistics and Financial Mathematics, Beijing Normal University, Beijing 100875, China |
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Abstract: | This paper mainly introduces the method of empirical likelihood and its applications on two different models. We discuss the empirical likelihood inference on fixed-effect parameter in mixed-effects model with error-in-variables. We first consider a linear mixed-effects model with measurement errors in both fixed and random effects. We construct the empirical likelihood confidence regions for the fixed-effects parameters and the mean parameters of random-effects. The limiting distribution of the empirical log likelihood ratio at the true parameter is χ p+q 2, where p, q are dimension of fixed and random effects respectively. Then we discuss empirical likelihood inference in a semi-linear error-in-variable mixed-effects model. Under certain conditions, it is shown that the empirical log likelihood ratio at the true parameter also converges to χ p+q 2. Simulations illustrate that the proposed confidence region has a coverage probability more closer to the nominal level than normal approximation based confidence region. |
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Keywords: | Confidence region empirical likelihood mixed-effects model |
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