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On the optimal choice of the number of empirical Fourier coefficients for comparison of regression curves

Author

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  • Viatcheslav Melas
  • Andrey Pepelyshev
  • Petr Shpilev
  • Luigi Salmaso
  • Livio Corain
  • Rosa Arboretti

Abstract

The paper is devoted to the elaboration of an efficient approach for comparison of two regression curves based on the empirical Fourier coefficients of regression functions. For the problem of testing for the equality of the two unknown functions in the case of homoscedastic error structure and observation at equidistant points, we derive a new procedure with adaptive choice of the number of the coefficients used in the hypotheses testing. Our approach is based on approximation of the most powerful test using the full knowledge of the regression functions. The results are justified by theoretical arguments and the superiority of the new procedure is also confirmed by a simulation study. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Viatcheslav Melas & Andrey Pepelyshev & Petr Shpilev & Luigi Salmaso & Livio Corain & Rosa Arboretti, 2015. "On the optimal choice of the number of empirical Fourier coefficients for comparison of regression curves," Statistical Papers, Springer, vol. 56(4), pages 981-997, November.
    • Handle: RePEc:spr:stpapr:v:56:y:2015:i:4:p:981-997
    DOI: 10.1007/s00362-014-0619-1
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    References listed on IDEAS

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    1. Teresa Ledwina & Grzegorz Wyłupek, 2012. "Two-Sample Test Against One-Sided Alternatives," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(2), pages 358-381, June.
    2. Fan J. & Huang L-S., 2001. "Goodness-of-Fit Tests for Parametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 640-652, June.
    3. Liang, Hua, 2004. "Comparison of curves based on a Cramer-von Mises statistic," Computational Statistics & Data Analysis, Elsevier, vol. 45(4), pages 805-812, May.
    4. Delgado, Miguel A., 1993. "Testing the equality of nonparametric regression curves," Statistics & Probability Letters, Elsevier, vol. 17(3), pages 199-204, June.
    5. King, Eileen & Hart, Jeffrey D. & Wehrly, Thomas E., 1991. "Testing the equality of two regression curves using linear smoothers," Statistics & Probability Letters, Elsevier, vol. 12(3), pages 239-247, September.
    6. J. Vilar-Fernández & J. Vilar-Fernández & W. González-Manteiga, 2007. "Bootstrap tests for nonparametric comparison of regression curves with dependent errors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 123-144, May.
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    Cited by:

    1. Rosa Arboretti & Riccardo Ceccato & Livio Corain & Fabrizio Ronchi & Luigi Salmaso, 2018. "Multivariate small sample tests for two-way designs with applications to industrial statistics," Statistical Papers, Springer, vol. 59(4), pages 1483-1503, December.

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