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

Abstract

This paper proposes a constrained empirical likelihood confidence region for a parameter β0 in the linear errors-in-variables model: Yi = xi τβ0 + Ei, 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. © 2003 Elsevier Science (USA). All rights reserved.