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An affine invariant k-nearest neighbor regression estimate

Author

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  • Biau, Gérard
  • Devroye, Luc
  • Dujmović, Vida
  • Krzyżak, Adam

Abstract

We design a data-dependent metric in Rd and use it to define the k-nearest neighbors of a given point. Our metric is invariant under all affine transformations. We show that, with this metric, the standard k-nearest neighbor regression estimate is asymptotically consistent under the usual conditions on k, and minimal requirements on the input data.

Suggested Citation

  • Biau, Gérard & Devroye, Luc & Dujmović, Vida & Krzyżak, Adam, 2012. "An affine invariant k-nearest neighbor regression estimate," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 24-34.
    • Handle: RePEc:eee:jmvana:v:112:y:2012:i:c:p:24-34
    DOI: 10.1016/j.jmva.2012.05.020
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    References listed on IDEAS

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    1. Thomas P. Hettmansperger, 2002. "A practical affine equivariant multivariate median," Biometrika, Biometrika Trust, vol. 89(4), pages 851-860, December.
    2. Davy Paindaveine & Germain Van Bever, 2012. "Nonparametrically Consistent Depth-Based Classifiers," Working Papers ECARES ECARES 2012-014, ULB -- Universite Libre de Bruxelles.
    3. Gordon, Louis & Olshen, Richard A., 1980. "Consistent nonparametric regression from recursive partitioning schemes," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 611-627, December.
    4. Hannu Oja, 1999. "Affine Invariant Multivariate Sign and Rank Tests and Corresponding Estimates: a Review," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(3), pages 319-343, September.
    5. Esa Ollila & Hannu Oja & Thomas P. Hettmansperger, 2002. "Estimates of regression coefficients based on the sign covariance matrix," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 447-466, August.
    6. Biau, Gérard & Devroye, Luc, 2010. "On the layered nearest neighbour estimate, the bagged nearest neighbour estimate and the random forest method in regression and classification," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2499-2518, November.
    7. Devroye, Luc & Krzyzak, Adam, 2002. "New Multivariate Product Density Estimators," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 88-110, July.
    8. Ollila E. & Oja H. & Koivunen V., 2003. "Estimates of Regression Coefficients Based on Lift Rank Covariance Matrix," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 90-98, January.
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    Cited by:

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    2. Ebner, Bruno & Henze, Norbert & Yukich, Joseph E., 2018. "Multivariate goodness-of-fit on flat and curved spaces via nearest neighbor distances," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 231-242.

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