【报告简介】We present a collection of interconnected methodologies for conducting non-parametric and semi-parametric statistical inference. While maximum likelihood estimation (MLE) is widely valued in parametric models for its strong consistency and optimality, these benefits weaken in cases of model misspecification or non-regularity. Moreover, the optimal properties of parametric MLE are established only for a local maximum of the likelihood function within a small neighborhood of the true parameter values, which is not fully satisfactory. Ideally, achieving a globally consistent maximum would be preferable.

To address the risks associated with model misspecification, one can adopt a semi-parametric framework and employ estimating functions within the empirical likelihood (EL) paradigm. However, the fundamental issue of MLE being merely a local maximum in the EL framework remains. In this work, we establish a set of clear conditions that guarantee the global consistency of the maximum. We propose a "global maximum test" to assess whether a given local maximum is indeed the global solution. Additionally, we introduce a "global maximum remedy," which improves global consistency by expanding the set of estimating functions within the EL framework.

【报告人介绍】Professor Jiahua Chen is a faculty member in the Department of Statistics at the University of British Columbia. His research interests span finite mixture models, statistical genetics, empirical likelihood, survey methodology, and experimental design, among others.

He is an elected Fellow of the Institute of Mathematical Statistics and the American Statistical Association. He has been recognized with the CRM-SSC Prize in Statistics for his outstanding contributions to the statistical sciences and received the Gold Medal, the top honor of the Statistical Society of Canada, in 2014. Additionally, he was awarded the International Chinese Statistical Association Distinguished Achievement Award in 2016 and was elected as a Fellow of the Royal Society of Canada in 2022.