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: Y-i = x(i)(tau) beta(0) + epsilon(i), X-i = x(i) + u(i), (1 less than or equal to i less than or equal to 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. (C) 2003 Elsevier Science (USA). All rights reserved.