函数型数据分析是统计学理论重要的研究方向.本项目拟开展函数型数据的指数有理样条处理方法(Expo-Rational B-Splines).以多元样条函数的渐近理论的研究为基础,发展一种系统研究函数型数据统计分析的多元指数有理样条方法. 用指数有理样条替代样条回归,从而处理大样本多个体的函数型数据.对图像函数型数据,利用张量积型的ERBS替代张量样条处理.结合两步核-样条等技术,开展对函数型数据的误差分布函数,误差方差函数等未知量进行统计推断的全新方法,并将其应用于医学图像处理、神经科学和运动医学中产生的脑电和心电等实际问题中.

Functional data analysis is an important research direction of statistical theory. This project intends to carry out the Expo Rational B-splines (ERBS) methods in the functional data analysis. Based on the asymptotic theory of multivariate spline theory, a multivariate Expo-Rational B-splines method is developed to systematically study the statistical analysis of functional data. Instead of the spline regression, the EBRS process the functional data with large sample and many individuals. For the image function data, the tensor product ERBS is used to replace the tensor spline processing. Combining the techniques of two-step kern-spline, a new method of statistical inference is developed for unknown variables such as error distribution function and error variance function of functional data. It is applied to the practical problems of electroencephalogram and electrocardiogram in medical image processing, neuroscience and sports medicine.