EMPIRICAL LIKELIHOOD CONFIDENCE REGION FOR PARAMETERS IN LINEAR ERRORS-IN-VARIABLES MODELS WITH MISSING DATA

The multivariate linear errors-in-variables model when the regressors are missing at random in the sense of Rubin(1976) is considered in this paper.A constrained empirical likelihood confidence region for a parameterβin this model is proposed,which is constructed by combining the score function corresponding to the weighted squared orthogonal distance based on inverse probability with a constrained region ofβ.It is shown that the empirical log-likelihood ratio at the true parameter converges to the standard chi-square distribution.Simulations show that the coverage rate of the proposed confidence region is closer to the nominal level and the length of confidence interval is narrower than those of the normal approximation of inverse probabihty weighted adjusted least square estimator in most cases.A real example is studied and the result supports the theory and simulation’s conclusion.