Empirical likelihood dimension reduction inference for partially non-linear error-in-responses models with validation data

In this article, partially non linear models when the response variable is measured with error and explanatory variables are measured exactly are considered. Without specifying any error structure equation, a semiparametric dimension reduction technique is employed. Two estimators of unknown parameter in non linear function are obtained and asymptotic normality is proved. In addition, empirical likelihood method for parameter vector is provided. It is shown that the estimated empirical log-likelihood ratio has asymptotic Chi-square distribution. A simulation study indicates that, compared with normal approximation method, empirical likelihood method performs better in terms of coverage probabilities and average length of the confidence intervals.