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Smoothed L-estimation of regression function

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  • Ci­zek, P.
  • Tamine, J.
  • Härdle, W.

Abstract

The Nadaraya-Watson nonparametric estimator of regression is known to be highly sensitive to the presence of outliers in data. This sensitivity can be reduced, for example, by using local L-estimates of regression. Whereas the local L-estimation is traditionally done using an empirical conditional distribution function, we propose to use instead a smoothed conditional distribution function. The asymptotic distribution of the proposed estimator is derived under mild [beta]-mixing conditions, and additionally, we show that the smoothed L-estimation approach provides computational as well as statistical finite-sample improvements. Finally, the proposed method is applied to the modelling of implied volatility.

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Bibliographic Info

Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 52 (2008)
Issue (Month): 12 (August)
Pages: 5154-5162

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Handle: RePEc:eee:csdana:v:52:y:2008:i:12:p:5154-5162

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References

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  1. Pavel Cizek & Wolfgang Härdle, 2005. "Robust estimation of dimension reduction space," SFB 649 Discussion Papers SFB649DP2005-015, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  2. Yacine Aït-Sahalia & Andrew W. Lo, 1998. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," Journal of Finance, American Finance Association, vol. 53(2), pages 499-547, 04.
  3. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339 Elsevier.
  4. Pavel Cizek & Wolfgang Karl Härdle & Rafal Weron, 2005. "Statistical Tools for Finance and Insurance," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0501.
  5. Lucas, Andre, 1995. "An outlier robust unit root test with an application to the extended Nelson-Plosser data," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 153-173.
  6. Tamine, Julien & Čížek, Pavel & Härdle, Wolfgang, 2002. "Smoothed L-estimation of regression function," SFB 373 Discussion Papers 2002,88, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  7. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, October.
  8. Matthias Fengler & Wolfgang Härdle & Christophe Villa, 2003. "The Dynamics of Implied Volatilities: A Common Principal Components Approach," Review of Derivatives Research, Springer, vol. 6(3), pages 179-202, October.
  9. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
  10. Michal Benko & Wolfgang Härdle, 2005. "Common Functional Implied Volatility Analysis," SFB 649 Discussion Papers SFB649DP2005-012, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  11. Shinichi Sakata & Halbert White, 1998. "High Breakdown Point Conditional Dispersion Estimation with Application to S&P 500 Daily Returns Volatility," Econometrica, Econometric Society, vol. 66(3), pages 529-568, May.
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Cited by:
  1. Cizek, P. & Tamine, J. & Härdle, W.K., 2006. "Smoothed L-estimation of Regression Function," Discussion Paper 2006-20, Tilburg University, Center for Economic Research.
  2. Mia Hubert & Irène Gijbels & Dina Vanpaemel, 2013. "Reducing the mean squared error of quantile-based estimators by smoothing," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 22(3), pages 448-465, September.

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