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Invariant tests for functional data with application to an earthquake impact study

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  • Huang, Wei-Hsueh
  • Huang, Li-Shan
  • Yang, Cheng-Tao

Abstract

Motivated by an earthquake impact study, this paper develops new tests with several invariant properties for functional data. For multi-sample functional ANOVA (mfANOVA), based on local polynomial regression, exact local and global ANOVA decompositions into within- and between-group of variations are obtained. A local mfANOVA test is developed to examine differences in a local neighborhood, and combining local quantities, a global mfANOVA test statistic is formed. We show that both the local and global mfANOVA test statistics are location, scale, and translation invariant, allow interchanging the order of smoothing and ANOVA projection, and have asymptotic F-distributions under the null hypotheses with the Gaussian assumption. This paper contributes to the literature by being the first, to our knowledge, to study mfANOVA tests with several invariant properties. Simulation studies are presented to compare the proposed global mfANOVA test with some existing procedures. Application to an earthquake impact study in Taiwan reveals that when an earthquake in 2016 resulted in closed highways, the patterns of traffic flows were significantly different between three time periods, before the earthquake, during, and after the repair period. The information could be useful in planning for disaster preparedness.

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  • Huang, Wei-Hsueh & Huang, Li-Shan & Yang, Cheng-Tao, 2022. "Invariant tests for functional data with application to an earthquake impact study," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:jmvana:v:189:y:2022:i:c:s0047259x2100172x
    DOI: 10.1016/j.jmva.2021.104894
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    References listed on IDEAS

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    1. 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.
    2. Muller, Hans-Georg & Stadtmuller, Ulrich & Yao, Fang, 2006. "Functional Variance Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1007-1018, September.
    3. Delsol, Laurent & Ferraty, Frédéric & Vieu, Philippe, 2011. "Structural test in regression on functional variables," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 422-447, March.
    4. Zhang, Jin-Ting & Cheng, Ming-Yen & Wu, Hau-Tieng & Zhou, Bu, 2019. "A new test for functional one-way ANOVA with applications to ischemic heart screening," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 3-17.
    5. Zambom, Adriano Zanin & Akritas, Michael G., 2017. "NonpModelCheck: An R Package for Nonparametric Lack-of-Fit Testing and Variable Selection," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 77(i10).
    6. J. Barrientos-Marin & F. Ferraty & P. Vieu, 2010. "Locally modelled regression and functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(5), pages 617-632.
    7. Tomasz Górecki & Łukasz Smaga, 2019. "fdANOVA: an R software package for analysis of variance for univariate and multivariate functional data," Computational Statistics, Springer, vol. 34(2), pages 571-597, June.
    8. Tomasz Górecki & Łukasz Smaga, 2015. "A comparison of tests for the one-way ANOVA problem for functional data," Computational Statistics, Springer, vol. 30(4), pages 987-1010, December.
    9. Kraus, David, 2019. "Inferential procedures for partially observed functional data," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 583-603.
    10. 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.
    11. Aneiros, Germán & Cao, Ricardo & Fraiman, Ricardo & Genest, Christian & Vieu, Philippe, 2019. "Recent advances in functional data analysis and high-dimensional statistics," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 3-9.
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