全函数型线性回归模型参数的可分解性检验

The Separability Test of Parameter for the Function-on-Function Linear Regression Model

本文提出一个可以用于检验函数型线性回归模型参数可分解性的方法.在参数的可分解性条件下,形成了一个新的函数型线性模型结构,此模型结构不仅降低全函数型线性模型的复杂度,还有利于对数据进行解释.构造的检验统计量主要基于模型参数在可分解结构与不可分解结构距离的范数.理论上证明了检验统计量在原假设和备择假设下的大样本性质.借助于Wild Bootstrap的重抽样技术,通过具体的模拟例子和实际数据分析来验证此检验方法的有效性.

This paper presents a test for the separability of the parameter of a functional linear regression model.Under the condition of separability,a new functional linear model structure is formed,which not only reduces the complexity of existing functional linear models,but also facilitates the inter-pretation of the data.The test statistic is constructed by using the norm of the distance between the separable and not separable structure of the model parameter.Theoretically,the large sample property of the test statistic is demonstrated under the null and alternative hypotheses.The validity of this test method is verified by simulation and real data analysis with the help of Wild Bootstrap techniques.