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Boundary Aware Estimators of Integrated Density Derivative Products

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  • Ming‐Yen Cheng

Abstract

Integrated squared density derivatives are important to the plug‐in type of bandwidth selector for kernel density estimation. Conventional estimators of these quantities are inefficient when there is a non‐smooth boundary in the support of the density. We introduce estimators that utilize density derivative estimators obtained from local polynomial fitting. They retain the rates of convergence in mean‐squared error that are familiar from non‐boundary cases, and the constant coefficients have similar forms. The estimators and the formula for their asymptotically optimal bandwidths, which depend on integrated products of density derivatives, are applied to automatic bandwidth selection for local linear density estimation. Simulation studies show that the constructed bandwidth rule and the Sheather–Jones bandwidth are competitive in non‐boundary cases, but the former overcomes boundary problems whereas the latter does not.

Suggested Citation

  • Ming‐Yen Cheng, 1997. "Boundary Aware Estimators of Integrated Density Derivative Products," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 191-203.
    • Handle: RePEc:bla:jorssb:v:59:y:1997:i:1:p:191-203
    DOI: 10.1111/1467-9868.00063
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    3. Tiee-Jian Wu & Chih-Yuan Hsu & Huang-Yu Chen & Hui-Chun Yu, 2014. "Root $$n$$ n estimates of vectors of integrated density partial derivative functionals," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(5), pages 865-895, October.
    4. Ghanem, Dalia & Zhang, Junjie, 2014. "‘Effortless Perfection:’ Do Chinese cities manipulate air pollution data?," Journal of Environmental Economics and Management, Elsevier, vol. 68(2), pages 203-225.
    5. Tomasz Olma, 2021. "Nonparametric Estimation of Truncated Conditional Expectation Functions," Papers 2109.06150, arXiv.org.
    6. Yu, X. & Zhang, X. & You, L., 2018. "Does The Granary County Subsidy Policy Lead to Manipulation of Grain Production Data in China? Evidence from a Natural Experiment," 2018 Conference, July 28-August 2, 2018, Vancouver, British Columbia 277298, International Association of Agricultural Economists.
    7. Zhang, Xiaoheng & Yu, Xiaohua & You, Liangzhi, 2020. "Does the Granary County Subsidy Program Lead to manipulation of grain production data in China?," China Economic Review, Elsevier, vol. 62(C).
    8. Lovett, Nicholas & Xue, Yuhan, 2022. "Rare homicides, criminal behavior, and the returns to police labor," Journal of Economic Behavior & Organization, Elsevier, vol. 194(C), pages 172-195.
    9. Bagkavos, Dimitrios & Ioannides, Dimitrios, 2021. "Fixed design local polynomial smoothing and bandwidth selection for right censored data," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).
    10. Dimitrios Bagkavos, 2011. "Local linear hazard rate estimation and bandwidth selection," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(5), pages 1019-1046, October.

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