Thresholding mean test for functional data with power enhancement
Thresholding mean test for functional data with power enhancement
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DOI：
10.1002/sta4.509
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发表时间：
2022-09
期刊：
影响因子：
1.7
通讯作者：
Qingsong Wang;Shaojun Guo;Fang Yao;Changliang Zou
中科院分区：
文献类型：
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作者：
Qingsong Wang;Shaojun Guo;Fang Yao;Changliang Zou
本文考虑了无穷维函数型数据的双样本均值检验问题，提出了一种新的检验方法。所提出的硬阈值检验统计量基于归一化函数主成分得分，并允许成分数量随样本量而异。硬阈值部分被引入用于功率改进。在原假设和局部替代假设下，得到了统计量的渐近正态性。我们还设计了一个基于L2范数的功率增强组件，以进一步减轻某些替代方案下的功率损失。我们进行了大量的数值模拟和分析一个真实的例子来证明所提出的测试的优越性，几个竞争对手。
We consider the two‐sample mean testing problem for infinite‐dimensional functional data and present a new testing procedure. The proposed hard‐thresholding test statistic is based on the normalized functional principal component scores and allows the number of components diverging with the sample size. The hard‐thresholding part is introduced for the power improvement. The asymptotic normality of the statistic is derived under both the null hypothesis and some local alternatives. We also design a power enhancement component based on L2 ‐norm to further alleviate the power loss under certain alternatives. We conduct extensive numerical simulations and analyze a real example to demonstrate the superiority of the proposed test to several competitors.