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Nonparametric estimation of conditional medians for linear and related processes


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  • Toshio Honda



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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Bibliographic Info

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

Volume (Year): 62 (2010)
Issue (Month): 6 (December)
Pages: 995-1021

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Handle: RePEc:spr:aistmt:v:62:y:2010:i:6:p:995-1021

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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. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  2. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(02), pages 186-199, June.
  3. 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.
  4. Honda, Toshio, 2006. "Nonparametric Density Estimation for Linear Processes with Infinite Variance," Discussion Papers 2005-13, Graduate School of Economics, Hitotsubashi University.
  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. 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.
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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, 2013. "Nonparametric quantile regression with heavy-tailed and strongly dependent errors," Annals of the Institute of Statistical Mathematics, Springer, vol. 65(1), pages 23-47, February.


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