复杂数据下联合均值与方差模型的统计推断

联合均值与方差模型是20世纪80年代发展起来的一类重要的统计模型，该模型既对感兴趣的均值参数建模,同时又对感兴趣的方差参数建模,可以概括和描述众多的实际问题。然而，在实践中,利用联合均值与方差模型解决实际问题的时候, 一方面常常会遇到缺失数据、测量误差数据、删失数据和纵向数据等复杂数据；另一方面，为了获得及时、准确的信息，往往还需考虑拟合复杂模型（如：非参、半参和变系数）的联合均值与方差模型。目前,大多数文献集中于复杂数据和复杂模型下均值回归模型的统计推断。为此本项目将从复杂数据和复杂模型的角度，针对联合均值与方差模型建立一套系统处理复杂数据的统计分析方法，重点讨论复杂数据下复杂联合均值与方差模型的估计理论、变量选择和经验似然推断方法及结合金融、经济、社会科学、气候科学、环境科学、工程技术和生物医学等学科中的一些实际复杂数据作相关统计分析，为这些学科的研究和发展提供新的统计分析方法。

Joint mean and variance models have been developed a kind of important statistical models since 1980s. This model is not only interested in the mean parameter modeling, but also interested in the variance parameter modeling. So a lot of actual problems can be described by this model. However, in practice, we often encounter some complicated data such as missing data, measurement error data, censored data, longitudinal data and so on when the joint mean and variance models is used to deal with the actual problems. On the other hand, in order to obtain timely, accurate information, we often need to be considered to model joint mean and variance models based on the complicatd statistics models (for example,nonparametric, semiparametric, varying coefficient). In statistical literature, many different approaches have been suggested to the problem of flexibly modeling of the mean based on the complicated data and structure. For this reason, we will study the estimated theory, variable selection and empirical likelihood inference for joint mean and variance models based on the complicated data and structure. We will further explore the applications of the obtained results in the finance, economics, sociology, climatology, environmetrics, engineering, and biomedical sciences, provide new statistical analysis method to the research and development of these disciplines.