复杂数据模型中的分布逼近方法

In this project, we mainly study distribution approximation methods and develop their theories based on some statistical models for complex data, which includes models as follows:(1)Generalized linear model; (2)Economitrical model (Tobit model) with limited response variable; (3)Survival model with censored data; (4)Complex longitudinal data model and (5)High-dimensional data model. From the backgroud of application, we plan to carry out research about statistic motivation, model construction, statistical method and theory and so on, in which we propose or improve the related statistical methods and furthermore study their asymptotic properties. Especially, it focuses on the asymptotic distribution of parameter estimate with nuisance parameter. Therefore, the issue of distribution approximation theory is intensively investigated to avoid to estimating the nuisance parameter. A new resampling approach techneque is presented for study of distribution approximation, while the proposed method not only has the efficience on the approximation, but also the ability on easy computation. These issues will lead to a series of future work which possesses importance of theory and application. All of the proposed methods will be evaluated by numerical studies and real data examples.

本项目主要研究若干基于复杂数据的统计模型中的分布逼近方法和其理论，其 中统计模型包括广义线性模型，响应变量受限制的计量经济模型（Tobit 模型）,生存分析中删失数据模型，各种复杂纵向数据模型和高维数据模型. 我们将结合各模型的应用背景，从统计思想，建模，方法和理论等方面进行研究，提出或改进有关的统计方法，深入研究它们的渐近性质，特别着重于带冗余参数的渐近分布的研究.因此,为避免冗余参数的估计，对有关的分布逼近理论问题进行深入的探索.我们将提出新的再抽样方法来进行分布逼近，新的方法既要保证逼近的有效性，同时还要易于计算. 这些问题将可引发一系列的后续研究工作,具有重要的理论意义和应用前景. 所提的方法都要通过数值计算和实际数据例子来验证其效果.

本项目主要研究了若干复杂数据下统计模型的渐近分布近似方法及其理论，其中研究成果包括建立了带有测量误差的广义线性模型的序贯估计和理论性质；获得了双尾截断Tobit模型的LAD估计的分布逼近方法和理论分析；提出了带有有效观测信息的左删失纵向数据的Tobit分位数估计的统计推断方法和组合分位数估计方法；建立了高维数据下Tobit模型估计方法和统计性质以及相对误差估计的统计分布推断方法等。这些研究成果已经发表在国内外高水平学术期刊上，所得结果对解决医学和计量经济学等实际问题提供有效的统计分析方法和可靠的理论支撑。