含有缺失的散度偏大计数数据的有限混合建模研究

项目名称： 含有缺失的散度偏大计数数据的有限混合建模研究

项目编号： No.11201200

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 付英姿

作者单位： 昆明理工大学

项目金额： 23万元

中文摘要： 本项目以生物医学、经济学、公共健康以及保险等领域中广泛存在的计数数据为研究对象，拟基于有限混合模型对含有缺失的散度偏大计数数据展开统计推断研究。具体而言，通过全面分析导致计数数据散度偏大成因，建立起上述数据的有限混合回归模型，以合理刻画数据的"非同质性"和"散度偏大"等特征；在此基础上，结合不同的缺失数据机制，拟分别从似然和Bayesian分析的角度进一步深入研究上述模型在混合个数估计、模型参数估计、统计诊断、局部影响分析以及模型选择方面的理论方法，希望建立有效的估计算法、合理的统计诊断度量以及模型选择标准。本项目的研究是当代统计学中热点问题的自然结合和推广，其相关研究不仅为复杂计数数据的有限混合研究提供理论和方法上的支持，还可能为实际工作者提供技术上的参考。其预期研究成果为论文，预计在国内外重要学术刊物上发表论6-9篇。

中文关键词： 计数数据；散度偏大；有限混合；缺失数据；贝叶斯分析

英文摘要： The count data are commonly encountered in a wide variety of disciplines, such as biomedical, ecomometrics, public health and insurance, etc. In this project, the overdispersed count data with missing values are studied based on finite mixture modeling approach. To be specific, by fully analyzing the causes for overdispersion of count data, a finite mixture regression model is established for accounting for the "heterogeneity" and "overdispersion" inherent in the data. And then, with different missingness mechanisms considered, several important issues, namely, mixture components estimation, parameter estimation, statistical inference, local inference analysis as well as model selection related to the above models are investigated. An efficient estimation algorithm and an appropriate diagnostical measure as well as a model selection criterion are to be developed both for likelihood-based method and Bayesian approach respectively. Our research is the natural extension and generalization of the hot issues in modern statistics. The corresponding results not only provide the necessary support for complex count data analysis and finite mixture modeling theoretically and methodologically, but also can be used for reference for practical workers in large. The expected research results include 6-9 papers which are to be

英文关键词： count data；overdispersion；finte mixture modeling；missing data；Bayesian analysis