Empirical Likelihood Confidence Region for Parameters in Semi-linear Errors-in-Variables Models

This paper proposes a constrained empirical likelihood confidence region for a

parameter in the semi-linear errors-in-variables model. The confidence region is constructed by

combining the score function corresponding to the squared orthogonal distance with a constraint on

the parameter, and it overcomes that the solution of limiting mean estimation equations is not

unique. It is shown that the empirical log likelihood ratio at the true parameter converges to the

standard chi-square distribution. Simulations show that the proposed confidence region has

coverage probability which is closer to the nominal level, as well as narrower than those of normal

approximation of generalized least squares estimator in most cases. A real data example is given.