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

This paper proposes a constrained empirical likelihood confidence region for a parameter [beta]0 in the linear errors-in-variables model: Yi=xi[tau][beta]0+[var epsilon]i,Xi=xi+ui,(1[less-than-or-equals, slant]i[less-than-or-equals, slant]n), which is constructed by combining the score function corresponding to the squared orthogonal distance with a constrained region of [beta]0. 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.