Empirical likelihood confidence region for parameter in the errors-in-variables models

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.