Seminar by Jiahua Chen

Global Consistency of Empirical Likelihood

We present a collection of interconnected and notable approaches for non-parametric or semi-parametric statistical inferences. Within parametric models, the MLE is held in high regard for its pronounced consistency and optimality. However, these advantages diminish when dealing with non-regular or incorrectly specified parametric models. Additionally, they are limited to MLEs that are local maxima of the likelihood function,
within a small neighborhood of the true parameter value. Naturally, having the MLE confined to being the consistent global maximum is more desirable.

To mitigate model mis-specification risks, one can assume a semi-parametric model and make inferences using estimating functions under the umbrella of empirical likelihood (EL). Nonetheless, the limitation of viewing the MLE as a local maximum of the EL persists. In this paper, we tackle this limitation by introducing a set of clear conditions that ensure global consistency of the maximum. We devise a "global maximum test" to determine whether the local maximum under consideration indeed qualifies as a global maximum. Furthermore, we devise a "global maximum remedy" that enhances global consistency by broadening the set of estimating functions within the EL framework.

Our comprehensive simulation experiments across numerous examples from existing literature solidly validate the effectiveness of the proposed approaches. Moreover, our methods offer superior solutions to problems investigated in the literature when compared to their parametric counterparts.

This talk is based on a project of my Ph.D student Jim Liang and the content will be part of the thesis.