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Estimation of the essential supremum of a regression function

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  • Kohler, Michael
  • Krzyzak, Adam
  • Walk, Harro

Abstract

Given an independent and identically distributed sample of the distribution of an -valued random vector (X,Y), the problem of estimation of the essential supremum of the corresponding regression function is considered. Estimates are constructed, which converge almost surely to this value whenever the dependent variable Y satisfies some weak integrability condition.

Suggested Citation

  • Kohler, Michael & Krzyzak, Adam & Walk, Harro, 2011. "Estimation of the essential supremum of a regression function," Statistics & Probability Letters, Elsevier, vol. 81(6), pages 685-693, June.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:6:p:685-693
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    References listed on IDEAS

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    1. Franke Jürgen & Diagne Mabouba, 2006. "Estimating market risk with neural networks," Statistics & Risk Modeling, De Gruyter, vol. 24(2), pages 233-253, December.
    2. Michael Kohler & Adam Krzyżak & Harro Walk, 2003. "Strong consistency of automatic kernel regression estimates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(2), pages 287-308, June.
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    Cited by:

    1. Hertel, Ida & Kohler, Michael, 2013. "Estimation of the optimal design of a nonlinear parametric regression problem via Monte Carlo experiments," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 1-12.
    2. Kohler, Michael & Krzyżak, Adam, 2015. "Estimation of a jump point in random design regression," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 247-255.

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