多元函数型数据的统计分析及其应用研究

随着测量工具的进步、数据收集和存储能力的提升，在许多应用领域，如化学计量学、生物计量学、气候、水文、环境等，我们能在越来越精细的分辨率下收集数据。由于这些数据可以近似视为曲线而被称为函数型数据。近十年来，大量的文献主要对一元函数型数据进行了统计分析，而关于多元函数型数据的讨论非常少。然而，在实际应用中，我们会遇到许多多元的情况，如空间数据。因而本项目致力于对多元函数型数据进行统计建模。主要研究内容为：(1)在带度量误差的离散观测下，研究空间线性模型的估计问题；(2)提出一个新的多元函数线性模型-局部空间函数线性模型并研究其估计方法；(3)将一元的函数型非参数模型推广到多元的情况；(4)建立空间函数型Logistic回归模型，并将该模型用于水文数据中，建立洪涝干旱灾害的风险评估模型。

With the advances of the measuring instruments and the improvement of data collecting and storage capacity, in many fields of applied sciences, such as chemometrics, biometrics, climate, hydrology, environment etc., we can collect the data at finer and finer resolution. Because these data can be approximated as the curves, the data is regarded as functional data. Over the past decade, a lot of literatures have mainly discussed the univariate functional data analysis, but there are very little literatures abour the multivariate functional data. However, in practical applications, the functionaldata that we deal with is multivariate, such as spatial data. Thus, our project is committed to analyse multivariate functional data. The main contents are as follows: (1) Study the estimated problem of the spatial functional linear model under the discrete observations with measurement error; (2) Propose a new multivariate functional linear model-local spatial function linear model and study the estimation method; (3) Extend the univariate functional nonparametric model to multivariate case; (4) Establish a spatial functional logistic regression model, and use this model to analyse the hydrological data and to assess the risk of the flood and drought disasters.