Empirical likelihood-based inference in nonlinear regression models with missing responses at random

Abstract

Abstract This paper investigates the estimations of regression parameters and response mean in nonlinear regression models in the presence of missing response variables that are missing with missingness probabilities depending on covariates. We propose four empirical likelihood (EL)-based estimators for the regression parameters and the response mean. The resulting estimators are shown to be consistent and asymptotically normal under some general assumptions. To construct the confidence regions for the regression parameters as well as the response mean, we develop four EL ratio statistics, which are proven to have the χ2 distribution asymptotically. Simulation studies and an artificial data set are used to illustrate the proposed methodologies. Empirical results show that the EL method behaves better than the normal approximation method and that the coverage probabilities and average lengths depend on the selection probability function. Keywords: confidence regionempirical likelihoodmissing at randomnonlinear regression modelsregression imputation Acknowledgements The authors thank the editor, an associate editor and two referees for their valuable suggestions which have greatly improved the paper. This work was supported by the grants from the National Natural Science Foundation of China, grant nos. 10961026, 11171293 and 2010CC003.