Empirical likelihood confidence region for parameter in the errors-in-variables models |
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Authors: | Hengjian Cui Song Xi Chen |
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Institution: | a Department of Mathematics, Beijing Normal University, Beijing 100875, China b Department of Statistics and Applied Probability, National University of Singapore, 117543, Singapore |
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Abstract: | This paper proposes a constrained empirical likelihood confidence region for a parameter β0 in the linear errors-in-variables model: Yi=xiτβ0+εi,Xi=xi+ui,(1?i?n), which is constructed by combining the score function corresponding to the squared orthogonal distance with a constrained region of β0. It is shown that the coverage error of the confidence region is of order n−1, and Bartlett corrections can reduce the coverage errors to n−2. An empirical Bartlett correction is given for practical implementation. Simulations show that the proposed confidence region has satisfactory coverage not only for large samples, but also for small to medium samples. |
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Keywords: | 62G05 62F12 |
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