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Nonparametric Estimation of Conditional Medians for Linear and Related Processes

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  • Honda, Toshio

Abstract

We consider nonparametric estimation of conditional medians for time series data. The time series data are generated from two mutually independent linear processes. The linear processes may show long-range dependence.The estimator of the conditional medians is based on minimizing the locally weighted sum of absolute deviations for local linear regression. We present the asymptotic distribution of the estimator. The rate of convergence is independent of regressors in our setting. The result of a simulation study is also given.

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File URL: http://hermes-ir.lib.hit-u.ac.jp/rs/bitstream/10086/16925/1/070econDP05-04.pdf
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Bibliographic Info

Paper provided by Graduate School of Economics, Hitotsubashi University in its series Discussion Papers with number 2005-04.

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Length: 31, [9] p.
Date of creation: Oct 2007
Date of revision:
Handle: RePEc:hit:econdp:2005-04

Note: September 2005; October 2007 (revised)
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Phone: +81-42-580-8000
Web page: http://www.econ.hit-u.ac.jp/
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Related research

Keywords: Local linear estimator; least absolute deviation regression; conditional quantiles; linear processes; short-range dependence; long-range dependence; random design; martingale CLT; simulation study;

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  1. Koul, Hira L. & Surgailis, Donatas, 2001. "Asymptotics of empirical processes of long memory moving averages with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 91(2), pages 309-336, February.
  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. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(02), pages 186-199, June.
  4. Koul, Hira L. & Baillie, Richard T. & Surgailis, Donatas, 2004. "Regression Model Fitting With A Long Memory Covariate Process," Econometric Theory, Cambridge University Press, vol. 20(03), pages 485-512, June.
  5. 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.
  6. Giraitis, Liudas & Koul, Hira L. & Surgailis, Donatas, 1996. "Asymptotic normality of regression estimators with long memory errors," Statistics & Probability Letters, Elsevier, vol. 29(4), pages 317-335, September.
  7. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  8. Peter Hall & Liang Peng & Qiwei Yao, 2002. "Prediction and nonparametric estimation for time series with heavy tails," LSE Research Online Documents on Economics 6086, London School of Economics and Political Science, LSE Library.
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Cited by:
  1. Honda, Toshio, 2013. "Nonparametric LAD cointegrating regression," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 150-162.
  2. Toshio Honda, 2010. "Nonparametric Quantile Regression with Heavy-Tailed and Strongly Dependent Errors," Global COE Hi-Stat Discussion Paper Series gd10-157, Institute of Economic Research, Hitotsubashi University.

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