B0886
Title: Global consistency of empirical likelihood
Authors: Jiahua Chen - University of British Columbia (Canada) [presenting]
Haodi Liang - University of British Columbia (Canada)
Abstract: The overwhelmingly favoured maximum likelihood estimator (MLE) under the parametric model is renowned for its strong consistency and optimality generally credited to Cramer. These properties, however, falter when the model is not regular or not completely accurate. In addition, their applicability is limited to local maxima close to the unknown true parameter value. One must therefore ascertain that the global maximum of the likelihood is strongly consistent under generic conditions. Global consistency is also a vital research problem in the context of empirical likelihood. The EL is a ground-breaking platform for non-parametric statistical inference. A subsequent milestone is achieved by placing estimating functions under the EL umbrella. The resulting profile EL function possesses many nice properties of parametric likelihood but also shares the same shortcomings. These properties cannot be utilized unless the known local maximum at hand is close to the unknown true parameter value. To overcome this obstacle, a clean set of conditions is first put forward under which the global maximum is consistent. A global maximum test is then developed to ascertain if the local maximum at hand is in fact a global maximum. Furthermore, a global maximum remedy is invented to ensure global consistency by expanding the set of estimating functions under EL. The simulation experiments firmly establish that the proposed approaches work as predicted.
