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A new test for functional one-way ANOVA with applications to ischemic heart screening

Author

Listed:
  • Zhang, Jin-Ting
  • Cheng, Ming-Yen
  • Wu, Hau-Tieng
  • Zhou, Bu

Abstract

Motivated by an ischemic heart screening problem, a new global test for one-way ANOVA in functional data analysis is studied. The test statistic is taken as the maximum of the pointwise F-test statistic over the interval the functional responses are observed. Nonparametric bootstrap, which is applicable in more general situations and easier to implement than parametric bootstrap, is employed to approximate the null distribution and to obtain an approximate critical value. Under mild conditions, asymptotically our test has the correct level and is root-n consistent in detecting local alternatives. Simulation studies show that the proposed test outperforms several existing tests in terms of both size control and power when the correlation between observations at any two different points is high or moderate, and it is comparable with the competitors otherwise. Application to an ischemic heart dataset suggests that resting electrocardiogram signals may contain enough information for ischemic heart screening at outpatient clinics, without the help of stress tests required by the current standard procedure.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:csdana:v:132:y:2019:i:c:p:3-17
    DOI: 10.1016/j.csda.2018.05.004
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    References listed on IDEAS

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    1. 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.
    2. Alonso, Andrés M. & Casado, David & Romo, Juan, 2012. "Supervised classification for functional data: A weighted distance approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2334-2346.
    3. E. Paparoditis & T. Sapatinas, 2016. "Bootstrap-based testing of equality of mean functions or equality of covariance operators for functional data," Biometrika, Biometrika Trust, vol. 103(3), pages 727-733.
    4. Dennis D. Cox & Jong Soo Lee, 2008. "Pointwise testing with functional data using the Westfall--Young randomization method," Biometrika, Biometrika Trust, vol. 95(3), pages 621-634.
    5. 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.
    6. Slaets, Leen & Claeskens, Gerda & Hubert, Mia, 2012. "Phase and amplitude-based clustering for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2360-2374.
    7. Stefan Fremdt & Josef G. Steinebach & Lajos Horváth & Piotr Kokoszka, 2013. "Testing the Equality of Covariance Operators in Functional Samples," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(1), pages 138-152, March.
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