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Penalized wavelet monotone regression

Author

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  • Antoniadis, Anestis
  • Bigot, Jéremie
  • Gijbels, Irène

Abstract

In this paper we focus on nonparametric estimation of a constrained regression function using penalized wavelet regression techniques. This results into a convex optimization problem under linear constraints. Necessary and sufficient conditions for existence of a unique solution are discussed. The estimator is easily obtained via the dual formulation of the optimization problem. In particular we investigate a penalized wavelet monotone regression estimator. We establish the rate of convergence of this estimator, and illustrate its finite sample performance via a simulation study. We also compare its performance with that of a recently proposed constrained estimator. An illustration to some real data is given.

Suggested Citation

  • Antoniadis, Anestis & Bigot, Jéremie & Gijbels, Irène, 2007. "Penalized wavelet monotone regression," Statistics & Probability Letters, Elsevier, vol. 77(16), pages 1608-1621, October.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:16:p:1608-1621
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    References listed on IDEAS

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    1. E. Mammen & C. Thomas‐Agnan, 1999. "Smoothing Splines and Shape Restrictions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(2), pages 239-252, June.
    2. Antoniadis, A. & Grégoire, G. & Vial, P., 1997. "Random design wavelet curve smoothing," Statistics & Probability Letters, Elsevier, vol. 35(3), pages 225-232, October.
    3. Gallant, A. Ronald, 1981. "On the bias in flexible functional forms and an essentially unbiased form : The fourier flexible form," Journal of Econometrics, Elsevier, vol. 15(2), pages 211-245, February.
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