标题： 基于$L^2$-范数的协方差函数相等性检验的进一步研究 显示英文标题

标题： A Further Study of an $L^2$-norm Based Test for the Equality of Several Covariance Functions

摘要： 对于多样本等协方差函数（ECF）检验问题，张（2013年）提出了一种基于$L^{2}$-范数的检验方法。然而，其渐近势和有限样本性能尚未被研究。本文在一些温和条件下探讨了该检验方法的渐近势。结果显示，基于$L^2$-范数的检验具有根-$n$一致性。此外，大量的模拟研究表明，在功能数据相关性较低或有效信号信息位于高频时，与弗雷姆特等人（2013年）提出的降维检验相比，基于$L^{2}$-范数的检验在控制检验水平和提高检验势方面表现更优。同时，还通过两个实际数据应用展示了基于$L^2$-范数的检验的良好性能。 显示英文摘要

摘要： For the multi-sample equal covariance function (ECF) testing problem, Zhang (2013) proposed an $L^{2}$-norm based test. However, its asymptotic power and finite sample performance have not been studied. In this paper, its asymptotic power is investigated under some mild conditions. It is shown that the $L^2$-norm based test is root-$n$ consistent. In addition, intensive simulation studies demonstrate that in terms of size-controlling and power, the $L^{2}$-norm based test outperforms the dimension-reduction based test proposed by Fremdt et al. (2013) when the functional data are less correlated or when the effective signal information is located in high frequencies. Two real data applications are also presented to demonstrate the good performance of the $L^2$-norm based test.