Abstract
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 ‐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.
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