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Local polynomial regression with correlated errors in random design and unknown correlation structure

Author

Listed:
  • K De Brabanter
  • F Cao
  • I Gijbels
  • J Opsomer

Abstract

SummaryAutomated or data-driven bandwidth selection methods tend to break down in the presence of correlated errors. While this problem has previously been studied in the fixed design setting for kernel regression, the results were applicable only when there is knowledge about the correlation structure. This article generalizes these results to the random design setting and addresses the problem in situations where no prior knowledge about the correlation structure is available. We establish the asymptotic optimality of our proposed bandwidth selection criterion based on kernels $K$ satisfying $K(0)=0$.

Suggested Citation

  • K De Brabanter & F Cao & I Gijbels & J Opsomer, 2018. "Local polynomial regression with correlated errors in random design and unknown correlation structure," Biometrika, Biometrika Trust, vol. 105(3), pages 681-690.
    • Handle: RePEc:oup:biomet:v:105:y:2018:i:3:p:681-690.
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    File URL: http://hdl.handle.net/10.1093/biomet/asy025
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    References listed on IDEAS

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    1. Tae Yoon Kim, 2004. "Nonparametric detection of correlated errors," Biometrika, Biometrika Trust, vol. 91(2), pages 491-496, June.
    2. I. Gijbels & A. Pope & M. P. Wand, 1999. "Understanding exponential smoothing via kernel regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 39-50.
    3. Byeong U. Park & Young Kyung Lee & Tae Yoon Kim & Cheolyong Park, 2006. "A Simple Estimator of Error Correlation in Non‐parametric Regression Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(3), pages 451-462, September.
    4. Peter Hall & Ingrid Van Keilegom, 2003. "Using difference‐based methods for inference in nonparametric regression with time series errors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 443-456, May.
    5. Kim, Tae Yoon & Park, Byeong U. & Moon, Myung Sang & Kim, Chiho, 2009. "Using bimodal kernel for inference in nonparametric regression with correlated errors," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1487-1497, August.
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    Cited by:

    1. Kris Brabanter & Farzad Sabzikar, 2021. "Asymptotic theory for regression models with fractional local to unity root errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(7), pages 997-1024, October.
    2. Bastian Schäfer, 2021. "Bandwidth selection for the Local Polynomial Double Conditional Smoothing under Spatial ARMA Errors," Working Papers CIE 146, Paderborn University, CIE Center for International Economics.
    3. Nagy, Stanislav & Ferraty, Frédéric, 2019. "Data depth for measurable noisy random functions," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 95-114.
    4. Justin Dang & Aman Ullah, 2023. "Generalized kernel regularized least squares estimator with parametric error covariance," Empirical Economics, Springer, vol. 64(6), pages 3059-3088, June.

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