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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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  1. 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.
  2. Cizek, P. & Härdle, W.K., 2005. "Robust Estimation of Dimension Reduction Space," Discussion Paper 2005-31, Tilburg University, Center for Economic Research.
  3. Hardle, W., 1992. "Applied Nonparametric Methods," Papers 9204, Catholique de Louvain - Institut de statistique.
  4. Ci­zek, P. & Tamine, J. & Härdle, W., 2008. "Smoothed L-estimation of regression function," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5154-5162, August.
  5. Yacine Ait-Sahalia & Andrew W. Lo, 2000. "Nonparametric Risk Management and Implied Risk Aversion," NBER Working Papers 6130, National Bureau of Economic Research, Inc.
  6. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521586115, October.
  7. Michal Benko & Wolfgang Härdle, 2005. "Common Functional Implied Volatility Analysis," SFB 649 Discussion Papers SFB649DP2005-012, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  8. 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.
  9. 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.
  10. Oliver LINTON, . "Applied nonparametric methods," Statistic und Oekonometrie 9312, Humboldt Universitaet Berlin.
  11. Yacine Ait-Sahalia & Andrew W. Lo, 1995. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," NBER Working Papers 5351, National Bureau of Economic Research, Inc.
  12. 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., 2008. "Smoothed L-estimation of regression function," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5154-5162, August.
  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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