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On uniform consistent estimators for convex regression

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  • Néstor Aguilera
  • Liliana Forzani
  • Pedro Morin

Abstract

A new nonparametric estimator of a convex regression function in any dimension is proposed and its uniform convergence properties are studied. We start by using any estimator of the regression function and convexify it by taking the convex envelope of a sample of the approximation obtained. We prove that the uniform rate of convergence of the estimator is maintained after the convexification is applied. The finite-sample properties of the new estimator are investigated by means of a simulation study and the application of the new method is demonstrated in examples.

Suggested Citation

  • Néstor Aguilera & Liliana Forzani & Pedro Morin, 2011. "On uniform consistent estimators for convex regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(4), pages 897-908.
    • Handle: RePEc:taf:gnstxx:v:23:y:2011:i:4:p:897-908
    DOI: 10.1080/10485252.2011.597506
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    References listed on IDEAS

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    5. Collomb, Gérard & Härdle, Wolfgang, 1986. "Strong uniform convergence rates in robust nonparametric time series analysis and prediction: Kernel regression estimation from dependent observations," Stochastic Processes and their Applications, Elsevier, vol. 23(1), pages 77-89, October.
    6. Sanjay Mehrotra & Jie Sun, 1990. "An Algorithm for Convex Quadratic Programming That Requires O ( n 3.5 L ) Arithmetic Operations," Mathematics of Operations Research, INFORMS, vol. 15(2), pages 342-363, May.
    7. Härdle, Wolfgang, 1989. "Asymptotic maximal deviation of M-smoothers," Journal of Multivariate Analysis, Elsevier, vol. 29(2), pages 163-179, May.
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    Cited by:

    1. Fabrizio Durante & Ostap Okhrin, 2014. "Estimation procedures for exchangeable Marshall copulas with hydrological application," SFB 649 Discussion Papers SFB649DP2014-014, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Wang, Yongqiao & Wang, Shouyang & Dang, Chuangyin & Ge, Wenxiu, 2014. "Nonparametric quantile frontier estimation under shape restriction," European Journal of Operational Research, Elsevier, vol. 232(3), pages 671-678.
    3. Alireza Ahmadabadi & Burcu Hudaverdi Ucer, 2017. "Bivariate nonparametric estimation of the Pickands dependence function using Bernstein copula with kernel regression approach," Computational Statistics, Springer, vol. 32(4), pages 1515-1532, December.
    4. Lee, Chia-Yen & Johnson, Andrew L. & Moreno-Centeno, Erick & Kuosmanen, Timo, 2013. "A more efficient algorithm for Convex Nonparametric Least Squares," European Journal of Operational Research, Elsevier, vol. 227(2), pages 391-400.

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