复杂数据半参数异方差混合效应模型的统计研究

Missing data, longitudinal data and other kinds of complex data are often occurred in biomedicine, sociologic, educational, econometrical and financial research and applications. Semiparametric heteroscedasticity mixed effects models are flexible generalization of heteroscedasticity regression models, mixed effects models and nonparametric regression models, which combine some advantages of parametric models, nonparamtric models and mixed models. Statistical inference for Semiparametric heteroscedasticity mixed effects models for these complex data and its applications will be studied in this project which includes (1) The algorithms of Bayesian estimations, model tests, Bayesian influence analysis and case deletion statistical diagnostic for Semiparametric heteroscedasticity mixed effects models and for heteroscedasticity mixed effects models with missing data; (2) The lilelihood inference and statistical diagnostic for heteroscedasticity mixed effects models with missing data; (3) The algorithms of Bayesian variable selection for heteroscedasticity mixed effects models with missing data; (4)The other estimations and properties for semiparametric heteroscedasticity mixed effects models; (5) Applications to the above methodologies in biomedicine, sociologic, educational, econometrical and financial research. The contents of the project are new topics in the modern Statistics which should be developed and extended. To the end, some new methodologies and results will be obtained which develop and extend the existed work.

生物医学、社会学、教育学、经济学和金融学等研究领域及实际应用中存在大量的缺失数据、纵向数据和其他类型的复杂数据。半参数异方差混合效应模型是异方差回归模型、混合效应模型和非参数回归模型的自然推广。该模型综合了参数模型、非参数模型和混合效应模型的诸多优点。本项目拟研究复杂数据半参数异方差混合效应模型的统计推断及应用。主要内容包括:(1)半参数异方差混合效应模型和带有缺失数据的异方差混合效应模型的贝叶斯估计、模型检验、局部影响分析、数据删除诊断方法;(2)带有缺失数据的异方差混合效应模型的似然推断及统计诊断方法;(3)带有缺失数据的异方差混合效应模型的贝叶斯变量选择方法;(4)半参数异方差混合效应模型的其他估计及性质;(5)上述理论和方法在生物医学、社会学、教育学、经济学和金融学等领域的实际应用。本项目的研究内容是近代统计学发展需要解决的一些新课题，其研究成果必将扩展和丰富统计学的理论和方法。

课题组围绕项目申请书和计划书展开研究，针对半参数异方差混合效应模型提出了一系列处理复杂异质数据、纵向数据和缺失数据的统计方法。半参数异方差混合效应模型是异方差(非线性)回归模型、混合效应模型和半参数(非参数)回归模型的自然推广。通过对本项目的研究，我们取得了多项研究成果，主要集中在带有异方差数据、缺失数据、纵向数据和其它复杂数据的半参数异方差混合效应模型的贝叶斯估计、变量选择、统计诊断和模型检验。并将这些理论和方法应用于生物医学、社会学、教育学、经济学、金融学等领域中。研究成果不仅扩宽了半参数异方差混合效应模型的应用范围，而且丰富了现代统计学的理论和方法。.在本项目的资助下，课题组在国内外重要期刊(或会议)上共发表(或在线发表)论文18篇,其中SCI论文2篇，EI论文3篇，北大中文核心期刊论文13篇。此外，课题组成员共晋升正高级或副高级职称3人。