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A class of grouped Brunk estimators and penalized spline estimators for monotone regression


  • Xiao Wang
  • Jinglai Shen


We study a class of monotone univariate regression estimators. We use B-splines to approximate an underlying regression function and estimate spline coefficients based on grouped data. We investigate asymptotic properties of two monotone estimators: a grouped Brunk estimator and a penalized monotone estimator. These estimators are consistent at the boundary and their mean square errors achieve optimal convergence rates under suitable assumptions of the true regression function. Asymptotic distributions are developed and are shown to be independent of spline degrees and the number of knots. Simulation results and car data illustrate performance of the proposed estimators. Copyright 2010, Oxford University Press.

Suggested Citation

  • Xiao Wang & Jinglai Shen, 2010. "A class of grouped Brunk estimators and penalized spline estimators for monotone regression," Biometrika, Biometrika Trust, vol. 97(3), pages 585-601.
  • Handle: RePEc:oup:biomet:v:97:y:2010:i:3:p:585-601

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    Cited by:

    1. Pang Du & Christopher F. Parmeter & Jeffrey S. Racine, 2012. "Nonparametric Kernel Regression with Multiple Predictors and Multiple Shape Constraints," Department of Economics Working Papers 2012-08, McMaster University.
    2. Cheng, Guang & Zhao, Yichuan & Li, Bo, 2012. "Empirical likelihood inferences for the semiparametric additive isotonic regression," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 172-182.

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