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Estimation of regression contour clusters--an application of the excess mass approach to regression

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  • Polonik, Wolfgang
  • Wang, Zailong

Abstract

The paper shows that the technique known as excess mass can be translated to non-parametric regression with random design in d-dimensional Euclidean space, where the regression function m is given by m(x)=E(Y|X=x),x[set membership, variant]Rd. The approach is applied to estimating regression contour clusters, which are sets where m exceeds a certain threshold value. This is accomplished without prior estimation of the regression function. Consistency of the resulting estimators is studied, and a functional central limit theorem for the excess mass is derived in the regression context.

Suggested Citation

  • Polonik, Wolfgang & Wang, Zailong, 2005. "Estimation of regression contour clusters--an application of the excess mass approach to regression," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 227-249, June.
    • Handle: RePEc:eee:jmvana:v:94:y:2005:i:2:p:227-249
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    References listed on IDEAS

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    1. Nolan, D., 1991. "The excess-mass ellipsoid," Journal of Multivariate Analysis, Elsevier, vol. 39(2), pages 348-371, November.
    2. Polonik, Wolfgang & Yao, Qiwei, 2000. "Conditional minimum volume predictive regions for stochastic processes," LSE Research Online Documents on Economics 6311, London School of Economics and Political Science, LSE Library.
    3. Ghislaine Gayraud & Judith Rousseau, 2002. "Nonparametric Bayesian Estimation of Level Sets," Working Papers 2002-03, Center for Research in Economics and Statistics.
    4. Cheng, Ming-Yen & Hall, Peter, 1998. "On mode testing and empirical approximations to distributions," Statistics & Probability Letters, Elsevier, vol. 39(3), pages 245-254, August.
    5. M.‐Y. Cheng & P. Hall, 1998. "Calibrating the excess mass and dip tests of modality," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(3), pages 579-589.
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    1. Burman, Prabir & Polonik, Wolfgang, 2009. "Multivariate mode hunting: Data analytic tools with measures of significance," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1198-1218, July.
    2. Dau, Hai Dang & Laloë, Thomas & Servien, Rémi, 2020. "Exact asymptotic limit for kernel estimation of regression level sets," Statistics & Probability Letters, Elsevier, vol. 161(C).

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