In this paper we propose statistical inference tools for the covariance operators of functional time series in the two sample and change point problem. In contrast to most of the literature, the focus of our approach is not testing the null hypothesis of exact equality of the covariance operators. Instead, we propose to formulate the null hypotheses in the form that “the distance between the operators is small”, where we measure deviations by the sup-norm. We provide powerful bootstrap tests for these type of hypotheses, investigate their asymptotic properties and study their finite sample properties by means of a simulation study.

中文翻译：

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检测功能时间序列协方差算子中的相关差异：一种超规范方法

在本文中，我们为两个样本和变化点问题中的功能时间序列协方差算子提供了统计推断工具。与大多数文献相反，我们方法的重点不是检验协方差算子精确相等的零假设。相反，我们建议以“运算符之间的距离很小”的形式来表达零假设，在这里我们用sup-norm来衡量偏差。我们为这些类型的假设提供有力的自举测试，研究其渐近性质，并通过模拟研究来研究其有限样本性质。