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Testing symmetry of a nonparametric bivariate regression function

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  • Melanie Birke
  • Holger Dette
  • Kristin Stahljans

Abstract

We propose a test for symmetry of a regression function with a bivariate predictor based on the L2 distance between the original function and its reflection. This distance is estimated by kernel methods and it is shown that under the null hypothesis as well as under the alternative the test statistic is asymptotically normally distributed. The finite sample properties of a bootstrap version of this test are investigated by means of a simulation study and a possible application in detecting asymmetries in grey-scale images is discussed.

Suggested Citation

  • Melanie Birke & Holger Dette & Kristin Stahljans, 2011. "Testing symmetry of a nonparametric bivariate regression function," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 547-565.
    • Handle: RePEc:taf:gnstxx:v:23:y:2011:i:2:p:547-565
    DOI: 10.1080/10485252.2010.539687
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    References listed on IDEAS

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    1. Peter Hall & Peihua Qiu & Christian Rau, 2008. "Tracking Edges, Corners and Vertices in an Image," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(1), pages 1-17, March.
    2. Birke, Melanie, 2008. "Central limit theorems for the integrated squared error of derivative estimators," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1903-1913, September.
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    Cited by:

    1. Birke, Melanie & Bissantz, Nicolai, 2012. "Testing for symmetries in multivariate inverse problems," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 236-253.

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