线性函数型回归模型及其相关问题研究

In recent years, more and more statisticians had paid considerable attention to the statistical methods and theoretical studies of the functional data analysis in the international statistical community, becoming a new research focus, including statistical methods, inference theory and practical application of many of the problems to be studied. The project study mainly several important topics of linear functional regression model. They include the estimation and testing of a linear functional regression models and hybrid models with dependent error, the estimation and test of linear functional regression models and the hybrid model when functional data have measurement error, variable selection of linear functional regression and the hybrid model, including variables selection problems with dependent error and function data with measurement error situations. These problems both practical value and theoretical significance, some research problems arestill gaps in the literature.

近年来，函数型数据的统计方法和理论研究受到国际统计界的极大关注，逐渐成为一个新研究热点，包括统计方法、推断理论和实际应用的许多问题尚待研究。本项目的主要研究线性函数型回归模型中的几个重要的课题，它们包括带有相依误差的线性函数型回归模型和混合模型的估计和检验问题、函数型数据带有测量误差时线性函数型回归模型和混合模型的估计和检验问题、线性函数型回归和混合模型（包括带有相依误差和函数型数据带有测量误差情形）的变量选元问题。这些问题既有实际应用价值，也有理论意义，有些研究问题在文献中还是空白。

本项目在四年研究期间，按照项目研究内容开展研究，在国内外高水平学术期刊上发表论文22篇（国际SCI期刊20篇），其中在统计学国际顶级期刊发表论文9篇，圆满完成了研究任务，实现项目的研究目标。在函数型回归模型残差序列的自相关检验、残差条件异方差类时间序列模型的参数估计模型拟合优度检验、几类函数型回归模型的参数估计和变量选择取得有国际影响的成果。