报告题目：Robustly enhancing density estimation through adaptive model averaging with density power divergence

报告人：邹国华

时间：10月9日 14：30-15：30

地点：bet365 106会议室

报告摘要：Effective density estimation plays a pivotal role in both statistics and machine learning by providing a foundational framework for understanding and modeling the underlying distribution of data. Over the past decades, how to estimate the density of the data has received considerable attention. However, the traditional parametric density estimation methods are usually built on maximum likelihood, which is highly sensitive to outliers. To address this issue, we develop a robust cross-validation (CV) density averaging method based on the density power divergence, which allows balancing the robustness and efficiency in estimation by a tuning parameter. To alleviate the computational burden, we derive an approximation to the CV criterion using influence function and Taylor expansion techniques. The proposed robust density model averaging estimator is demonstrated to be asymptotically optimal in terms of minimizing the out-of-sample estimation error. Furthermore, we establish that the resultant weight estimator converges to the theoretically optimal weight vector. Additionally, in the case where the candidate model set includes the true density function, we demonstrate that the proposed density model averaging estimator is consistent with the true density function. The influence function of our density model averaging estimator is also derived. We evaluate the proposed technique on both simulated datasets and a real world rainfall dataset from Sutton Bonington, England. The results show that our method outperforms some commonly used estimation techniques in the presence of outliers.

报告人简介：邹国华，首都师范大学教授。博士毕业于中国科学院系统科学研究所，是国家杰出青年基金获得者、“新世纪百千万人才工程”国家级人选、中国科学院“百人计划”入选者、享受国务院政府特殊津贴，先后获中国科学院和北京市优秀研究生指导教师称号。

主要从事统计学的理论研究及其在经济金融、生物医学中的应用研究工作，在统计模型选择与平均、抽样调查的设计与分析、决策函数的优良性、疾病与基因的关联分析等方面的研究中取得了一系列重要成果，得到了国内外同行的好评与肯定，并被广泛引用。共出版教材2本，发表学术论文140余篇；主持和参加国家科学基金项目以及全国性的实际课题30余项，提出的预测方法被实际部门所采用。