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Depth notions for orthogonal regression

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  • Wellmann, Robin
  • Müller, Christine H.

Abstract

Global depth, tangent depth and simplicial depths for classical and orthogonal regression are compared in examples, and properties that are useful for calculations are derived. The robustness of the maximum simplicial depth estimates is shown in examples. Algorithms for the calculation of depths for orthogonal regression are proposed, and tests for multiple regression are transferred to orthogonal regression. These tests are distribution free in the case of bivariate observations. For a particular test problem, the powers of tests that are based on simplicial depth and tangent depth are compared by simulations.

Suggested Citation

  • Wellmann, Robin & Müller, Christine H., 2010. "Depth notions for orthogonal regression," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2358-2371, November.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:10:p:2358-2371
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    References listed on IDEAS

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    1. Wellmann, Robin & Müller, Christine H., 2010. "Tests for multiple regression based on simplicial depth," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 824-838, April.
    2. Ivan Mizera & Christine H. Muller, 2004. "Location-Scale Depth," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 949-966, December.
    3. Wellmann, Robin & Harmand, Peter & Müller, Christine H., 2009. "Distribution-free tests for polynomial regression based on simplicial depth," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 622-635, April.
    4. Van Aelst, Stefan & Rousseeuw, Peter J. & Hubert, Mia & Struyf, Anja, 2002. "The Deepest Regression Method," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 138-166, April.
    5. Müller, Christine H., 2005. "Depth estimators and tests based on the likelihood principle with application to regression," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 153-181, July.
    6. Wellmann, R. & Katina, S. & Muller, Ch.H., 2007. "Calculation of simplicial depth estimators for polynomial regression with applications," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 5025-5040, June.
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    Cited by:

    1. Christoph Kustosz & Christine Müller, 2014. "Analysis of crack growth with robust, distribution-free estimators and tests for non-stationary autoregressive processes," Statistical Papers, Springer, vol. 55(1), pages 125-140, February.

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