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Nonparametric Quantile Regression with Heavy-Tailed and Strongly Dependent Errors

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  • Toshio Honda

Abstract

We consider nonparametric estimation of the conditional qth quantile for stationary time series. We deal with stationary time series with strong time dependence and heavy tails under the setting of random design. We estimate the conditional qth quantile by local linear regression and investigate the asymptotic properties. It is shown that the asymptotic properties are affected by both the time dependence and the tail index of the errors. The results of a small simulation study are also given.

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File URL: http://gcoe.ier.hit-u.ac.jp/research/discussion/2008/pdf/gd10-157.pdf
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Bibliographic Info

Paper provided by Institute of Economic Research, Hitotsubashi University in its series Global COE Hi-Stat Discussion Paper Series with number gd10-157.

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Date of creation: Dec 2010
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Handle: RePEc:hst:ghsdps:gd10-157

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Keywords: conditional quantile; random design; check function; local linear regression; stable distribution; linear process; long-range dependence; martingale central limit theorem;

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  1. Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 143-156, Fall.
  2. Toshio Honda, 2009. "Nonparametric density estimation for linear processes with infinite variance," Annals of the Institute of Statistical Mathematics, Springer, vol. 61(2), pages 413-439, June.
  3. Liang Peng & Qiwei Yao, 2004. "Nonparametric regression under dependent errors with infinite variance," Annals of the Institute of Statistical Mathematics, Springer, vol. 56(1), pages 73-86, March.
  4. Ngai Chan & Rongmao Zhang, 2009. "M-estimation in nonparametric regression under strong dependence and infinite variance," Annals of the Institute of Statistical Mathematics, Springer, vol. 61(2), pages 391-411, June.
  5. Toshio Honda, 2010. "Nonparametric estimation of conditional medians for linear and related processes," Annals of the Institute of Statistical Mathematics, Springer, vol. 62(6), pages 995-1021, December.
  6. Härdle, Wolfgang K. & Song, Song, 2010. "Confidence Bands In Quantile Regression," Econometric Theory, Cambridge University Press, vol. 26(04), pages 1180-1200, August.
  7. Toshio Honda, 2000. "Nonparametric Estimation of a Conditional Quantile for α-Mixing Processes," Annals of the Institute of Statistical Mathematics, Springer, vol. 52(3), pages 459-470, September.
  8. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
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