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Nonparametric estimation in a regression model with additive and multiplicative noise

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  • Christophe Chesneau
  • Salima El Kolei
  • Junke Kou
  • Fabien Navarro

Abstract

In this paper, we consider an unknown functional estimation problem in a general nonparametric regression model with the characteristic of having both multiplicative and additive noise. We propose two wavelet estimators, which, to our knowledge, are new in this general context. We prove that they achieve fast convergence rates under the mean integrated square error over Besov spaces. The rates obtained have the particularity of being established under weak conditions on the model. A numerical study in a context comparable to stochastic frontier estimation (with the difference that the boundary is not necessarily a production function) supports the theory.

Suggested Citation

  • Christophe Chesneau & Salima El Kolei & Junke Kou & Fabien Navarro, 2019. "Nonparametric estimation in a regression model with additive and multiplicative noise," Papers 1906.07695, arXiv.org.
  • Handle: RePEc:arx:papers:1906.07695
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    File URL: http://arxiv.org/pdf/1906.07695
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    References listed on IDEAS

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    1. Léopold Simar & Valentin Zelenyuk, 2011. "Stochastic FDH/DEA estimators for frontier analysis," Journal of Productivity Analysis, Springer, vol. 36(1), pages 1-20, August.
    2. GIJBELS, Irène & MAMMEN, Enno & PARK, Byeong U. & SIMAR, Léopold, 1997. "On estimation of monotone and concave frontier functions," CORE Discussion Papers 1997031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Cai, T. Tony & Brown, Lawrence D., 1999. "Wavelet estimation for samples with random uniform design," Statistics & Probability Letters, Elsevier, vol. 42(3), pages 313-321, April.
    4. Daouia, Abdelaati & Simar, Léopold, 2005. "Robust nonparametric estimators of monotone boundaries," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 311-331, October.
    5. Fabien Navarro & Adrien Saumard, 2017. "Slope heuristics and V-Fold model selection in heteroscedastic regression using strongly localized bases," Working Papers 2017-67, Center for Research in Economics and Statistics.
    6. Girard, Stéphane & Jacob, Pierre, 2008. "Frontier estimation via kernel regression on high power-transformed data," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 403-420, March.
    7. Girard, Stéphane & Guillou, Armelle & Stupfler, Gilles, 2013. "Frontier estimation with kernel regression on high order moments," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 172-189.
    8. Hardle, W. & Tsybakov, A., 1997. "Local polynomial estimators of the volatility function in nonparametric autoregression," Journal of Econometrics, Elsevier, vol. 81(1), pages 223-242, November.
    9. Fan, Yanqin & Li, Qi & Weersink, Alfons, 1996. "Semiparametric Estimation of Stochastic Production Frontier Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 460-468, October.
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