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Local M-estimator for nonparametric time series

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  • Cai, Zongwu
  • Ould-Saïd, Elias

Abstract

In this article, we investigate a robust version of local linear regression smoothers for stationary time series sequence by using robust-type local polynomial techniques. Under some regularity conditions, we establish the weak and strong consistency as well as the asymptotic normality of the proposed estimators.

Suggested Citation

  • Cai, Zongwu & Ould-Saïd, Elias, 2003. "Local M-estimator for nonparametric time series," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 433-449, December.
    • Handle: RePEc:eee:stapro:v:65:y:2003:i:4:p:433-449
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    References listed on IDEAS

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    1. Cunningham, J. K. & Eubank, R. L. & Hsing, T., 1991. "M-type smoothing splines with auxiliary scale estimation," Computational Statistics & Data Analysis, Elsevier, vol. 11(1), pages 43-51, January.
    2. Masry, Elias & Tjøstheim, Dag, 1997. "Additive Nonlinear ARX Time Series and Projection Estimates," Econometric Theory, Cambridge University Press, vol. 13(2), pages 214-252, April.
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    5. Cai, Zongwu, 2003. "Nonparametric estimation equations for time series data," Statistics & Probability Letters, Elsevier, vol. 62(4), pages 379-390, May.
    6. P. M. Robinson, 1983. "Nonparametric Estimators For Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 185-207, May.
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    Cited by:

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    2. Yebin Cheng & Jan G. De Gooijer & Dawit Zerom, 2011. "Efficient Estimation of an Additive Quantile Regression Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(1), pages 46-62, March.
    3. Gheriballah, Abdelkader & Laksaci, Ali & Sekkal, Soumeya, 2013. "Nonparametric M-regression for functional ergodic data," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 902-908.
    4. Xiangdong Long & Liangjun Su & Aman Ullah, 2011. "Estimation and Forecasting of Dynamic Conditional Covariance: A Semiparametric Multivariate Model," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 109-125, January.
    5. Wang, Yunyan & Zhang, Lixin & Tang, Mingtian, 2012. "Local M-estimation for jump-diffusion processes," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1273-1284.
    6. Aman Ullah & Tao Wang & Weixin Yao, 2022. "Nonlinear modal regression for dependent data with application for predicting COVID‐19," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(3), pages 1424-1453, July.
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    8. Jia Chen & Li-Xin Zhang, 2010. "Local linear M-estimation for spatial processes in fixed-design models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 71(3), pages 319-340, May.
    9. Shangyu Xie & Yong Zhou & Alan T. K. Wan, 2014. "A Varying-Coefficient Expectile Model for Estimating Value at Risk," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(4), pages 576-592, October.
    10. Chen, Jia, 2008. "Asymptotics of kernel density estimators on weakly associated random fields," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3230-3237, December.
    11. Zhengyan Lin & Degui Li & Jiti Gao, 2009. "Local Linear M‐estimation in non‐parametric spatial regression," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(3), pages 286-314, May.
    12. Chen, Jia & Li, Degui & Zhang, Lixin, 2010. "Robust estimation in a nonlinear cointegration model," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 706-717, March.
    13. Zongwu Cai & Qi Li, 2013. "Some Recent Develop- ments on Nonparametric Econometrics," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    14. Yudong Wang & Zhiyuan Pan & Chongfeng Wu, 2017. "Time‐Varying Parameter Realized Volatility Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 36(5), pages 566-580, August.
    15. Battaglia, Francesco, 2005. "Outliers in functional autoregressive time series," Statistics & Probability Letters, Elsevier, vol. 72(4), pages 323-332, May.

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