函数型数据独立性的检验

A Procedure of TestingI nI dependence for Functional Variables

本文提出了一个可以用于函数型数据独立性检验的方法,该方法可以把函数型数据独立性的检验转化为向量型数据独立性的检验。为此所有适用于向量型数据独立性检验的方法都可以通过本文的方法用于函数型数据独立性的检验。该检验方法操作简单,而且在检验函数型数据的独立性时有更多选择。模拟显示,在某些情形下,用本文方法选择合适的独立性检验工具,相比选择那些只适合函数型数据的独立性检验方法,比如,距离协方差和球协方差,可以显著提高检验的功效。文中还给出了一个实例分析展示了所提出的检验方法在实际中的应用。

We propose an independence test procedure for functional variables which converts testing independence of two functional variables to testing independence between two random vectors.This means that any independence test tool designed for random vectors can be applied to functional variables.This test procedure is easily implemented and gives us more choice for choosing independence test methods.Simulations show that in some cases,with appropriate choice of independence test methods,one can improve the performance of the tests that only use those suitable for functional data,such as distance covariance and ball covariance.Additionally,a real data example is given to demonstrate the application of the proposed method.