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Nonparametric quantile regression with heavy-tailed and strongly dependent errors

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  • Toshio Honda

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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. Copyright The Institute of Statistical Mathematics, Tokyo 2013

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File URL: http://hdl.handle.net/10.1007/s10463-012-0359-8
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Bibliographic Info

Article provided by Springer in its journal Annals of the Institute of Statistical Mathematics.

Volume (Year): 65 (2013)
Issue (Month): 1 (February)
Pages: 23-47

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Handle: RePEc:spr:aistmt:v:65:y:2013:i:1:p:23-47

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Related research

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. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, 9.
  2. Ngai Chan & Rongmao Zhang, 2009. "M-estimation in nonparametric regression under strong dependence and infinite variance," Annals of the Institute of Statistical Mathematics, Springer, Springer, vol. 61(2), pages 391-411, June.
  3. Härdle, Wolfgang K. & Song, Song, 2010. "Confidence Bands In Quantile Regression," Econometric Theory, Cambridge University Press, vol. 26(04), pages 1180-1200, August.
  4. Honda, Toshio, 2007. "Nonparametric Estimation of Conditional Medians for Linear and Related Processes," Discussion Papers 2005-04, Graduate School of Economics, Hitotsubashi University.
  5. Toshio Honda, 2000. "Nonparametric Estimation of a Conditional Quantile for α-Mixing Processes," Annals of the Institute of Statistical Mathematics, Springer, Springer, vol. 52(3), pages 459-470, September.
  6. Honda, Toshio, 2006. "Nonparametric Density Estimation for Linear Processes with Infinite Variance," Discussion Papers 2005-13, Graduate School of Economics, Hitotsubashi University.
  7. Liang Peng & Qiwei Yao, 2004. "Nonparametric regression under dependent errors with infinite variance," Annals of the Institute of Statistical Mathematics, Springer, Springer, vol. 56(1), pages 73-86, March.
  8. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, Econometric Society, vol. 46(1), pages 33-50, January.
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