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Nonparametric derivative estimation with bimodal kernels under correlated errors

Author

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  • Deru Kong

    (Qufu Normal University)

  • Shengli Zhao

    (Qufu Normal University)

  • WenWu Wang

    (Qufu Normal University)

Abstract

For the derivative estimation, nonparametric regression with unimodal kernels performs well under independent errors, while it breaks down under correlated errors. In this paper, we propose the local polynomial regression based on bimodal kernels for the derivative estimation under correlated errors. Unlike the conventional local polynomial estimator, the proposed estimator does not require any prior knowledge about the correlation structure of errors. For the proposed estimator, we deduce the main theoretical results, including the asymptotic bias, asymptotic variance, and asymptotic normality. Based on the asymptotic mean integrated squared error, we also provide a data-driven bandwidth selection criterion. Subsequently, we compare three popular bimodal kernels from the robustness and efficiency. Simulation studies show that the heavy-tailed bimodal kernel is more robust and efficient than the other two bimodal kernels and two popular unimodal kernels, especially for high-frequency oscillation functions. Finally, two real data examples are presented to illustrate the feasibility of the proposed estimator.

Suggested Citation

  • Deru Kong & Shengli Zhao & WenWu Wang, 2024. "Nonparametric derivative estimation with bimodal kernels under correlated errors," Computational Statistics, Springer, vol. 39(4), pages 1847-1865, June.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:4:d:10.1007_s00180-023-01419-4
    DOI: 10.1007/s00180-023-01419-4
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    References listed on IDEAS

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    1. Sebastian Calonico & Matias D. Cattaneo & Max H. Farrell, 2018. "On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 767-779, April.
    2. Liu, Sisheng & Kong, Xiaoli, 2022. "A generalized correlated Cp criterion for derivative estimation with dependent errors," Computational Statistics & Data Analysis, Elsevier, vol. 171(C).
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    4. 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.
    5. Garritt L. Page & María Xosé Rodríguez‐Álvarez & Dae‐Jin Lee, 2020. "Bayesian hierarchical modelling of growth curve derivatives via sequences of quotient differences," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(2), pages 459-481, April.
    6. 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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