报告题目：Model Averaging Estimation for Probability Density Functions

主 讲 人：邹国华

单 位：首都师范大学

时 间：12月10日9:00

地 点：学院二楼会议室

腾 讯 ID：117 274 849

摘 要：

Extraction of information from data is critical in the age of data science. Theoretically probability density function provides comprehensive information on the data. But, practically, different probability density models, either parametric or non-parametric, though well estimated (depending on choice of parametric density forms or nonparametric density bandwidths), can often only characterize partial features on the data. In this paper we hence suggest a framework to optimally combine different density models to more comprehensively catch the data features in information extraction in the sense that the resultant density averaging or selected density minimises the Kullback-Leibler (KL) information loss function. We therefore first propose an estimator of the KL loss function, which takes the Akaike and Takeuchi information criteria as two special cases. Built on this new KL loss estimator, a feasible density model averaging (DMA) procedure is accordingly suggested. The optimality of the DMA estimation is further established which achieves the lowest possible KL loss asymptotically, and the consistency of the weights of the DMA estimator tending to the optimal averaging weights minimizing the KL distance is obtained. The convergence rate of the new empirical weights is also derived. Simulation studies show that the DMA performs overall better and more robustly than the commonly used parametric or nonparametric density models, including kernel, finite mixture and selection methods for density estimation in the literature. The analysis of two real data sets further demonstrates the performance of the proposed method.

简 介：

邹国华，首都师范大学特聘教授。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，曾获中国科学院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。目前出版教材1本，在《中国科学》、Biometrika、Genetics、INFORMS Journal on Computing、JASA、Journal of Econometrics等国内外顶级期刊上发表论文110余篇；主持和参加过近30项国家科学基金项目以及全国性的实际课题，提出的预测方法被实际部门所采用。