Empirical likelihood for nonlinear model with missing responses
Résumé
A nonlinear model with response variables missing at random is studied. In order to improve the coverage accuracy for model parameters, the empirical likelihood (EL) ratio method is considered. On the complete data, the EL statistic for the parameters and its approximation have a $\chi^2$ asymptotic distribution. When the response are reconstituted using a semi-parametric method, the empirical log-likelihood on the response variable associated on imputed data is also asymptotically $\chi^2$. The Wilk's theorem for EL on the parameters, based on reconstituted data, is also satisfied. These results can be used to construct the confidence region for the model parameters and for the response variable. It is shown via Monte Carlo simulations that the EL methods outperform the normal approximation based method in terms of coverage for the unknown parameter, inclusively on the reconstituted data. The advantages of the proposed method are exemplified on the real data.