An L2 -norm-based test for equality of several covariance functions: a further study

• Jia Guo ^[1] ; Bu Zhou ^[2] ; Jianwei Chen ^[3] ; Jin-Ting Zhang ^[4]
  1. [1] Zhejiang University of Technology

     Zhejiang University of Technology

     China

     
  2. [2] Zhejiang Gongshang University

     Zhejiang Gongshang University

     China

     
  3. [3] San Diego State University

     San Diego State University

     Estados Unidos

     
  4. [4] National University of Singapore

     National University of Singapore

     Singapur

     

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• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 28, Nº. 4, 2019, págs. 1092-1112
• Idioma: inglés
• DOI: 10.1007/s11749-018-0617-z
• Texto completo no disponible (Saber más ...)
• Resumen

  • For the multi-sample equal covariance function (ECF) testing problem, Zhang (Analysis of variance for functional data, CRC Press, Boca Raton, 2013) proposed an L2 -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 L2 -norm-based test is root-n consistent. In addition, intensive simulation studies are conducted to evaluate its finite sample performance against several existing competitors. In particular, they demonstrate that in terms of size control and power, the L2 -norm-based test outperforms the dimension-reduction-based tests proposed by Panaretos et al. (J Am Stat Assoc 105(490):670–682, 2010) and Fremdt et al. (Scand J Stat 40(1):138–152, 2013), respectively, when functional data are less correlated or when the covariance function differences of functional data contain mainly high-frequency signals. Two real data applications are presented to illustrate the L2 -norm-based test