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One-Way anova for Functional Data via Globalizing the Pointwise F-test

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  • Jin-Ting Zhang
  • Xuehua Liang

Abstract

type="main" xml:id="sjos12025-abs-0001"> In this paper, we propose and study a new global test, namely, GPF test, for the one-way anova problem for functional data, obtained via globalizing the usual pointwise F-test. The asymptotic random expressions of the test statistic are derived, and its asymptotic power is investigated. The GPF test is shown to be root-n consistent. It is much less computationally intensive than a parametric bootstrap test proposed in the literature for the one-way anova for functional data. Via some simulation studies, it is found that in terms of size-controlling and power, the GPF test is comparable with two existing tests adopted for the one-way anova problem for functional data. A real data example illustrates the GPF test.

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  • Jin-Ting Zhang & Xuehua Liang, 2014. "One-Way anova for Functional Data via Globalizing the Pointwise F-test," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 51-71, March.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:1:p:51-71
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    File URL: http://hdl.handle.net/10.1111/sjos.12025
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    1. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
    2. Cuevas, Antonio & Febrero, Manuel & Fraiman, Ricardo, 2004. "An anova test for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 47(1), pages 111-122, August.
    3. Jin-Ting Zhang, 2005. "Approximate and Asymptotic Distributions of Chi-Squared-Type Mixtures With Applications," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 273-285, March.
    4. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
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