稀疏设计下部分函数型线性模型的估计

发布时间：2017-12-30 18:27

本文关键词：稀疏设计下部分函数型线性模型的估计　出处：《华东师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：过去几十年里,函数型数据分析受到越来越多的重视,这些数据的每一个个体或试验单元都可以近似地看成一条曲线。函数型数据可以分为稠密观测和稀疏观测的数据,其中稀疏函数型数据指的是稀疏、不规则的且有测量误差的数据。函数型回归模型是函数型数据分析中重要的研究课题,但是目前关于函数型回归模型的研究大部分局限于完全观测或者稠密观测的函数型数据,而稀疏设计下的函数型回归模型的研究还很少。本文着重研究稀疏设计下部分函数型线性模型的估计,具体将采用函数型主成分分析和非参数统计中的局部线性方法,得到模型中参数和斜率函数的估计,并且将线性回归中可决系数的概念推广到部分函数型线性模型中,给出了估计方法,然后研究了这些估计量的大样本性质,最后通过数值模拟来说明所提出的估计方法有很好的有限样本性质。
[Abstract]:In the past several ten years, more and more attention has been paid to the analysis of functional data. Each individual or experimental unit of these data can be regarded as a curve approximately. Functional data can be divided into dense observation and sparse observation data, where sparse function data refers to sparse data. The functional regression model is an important research topic in the functional data analysis. However, most of the researches on the functional regression model are limited to the full or dense observation of the functional data. In this paper, we focus on the estimation of partial functional linear models in sparse design. The estimation of parameter and slope function in the model will be obtained by using the local linear method of functional principal component analysis and non-parametric statistics. Furthermore, the concept of determinable coefficients in linear regression is extended to partial functional linear models, and the estimation methods are given, and the large sample properties of these estimators are studied. Finally, numerical simulation shows that the proposed estimation method has good finite sample properties.
【学位授予单位】：华东师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

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