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Some improvements on a boundary corrected kernel density estimator

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  • Karunamuni, R.J.
  • Zhang, S.

Abstract

In a very interesting article, Zhang et al. [1999. An improved estimator of the density function at the boundary. J. Amer. Statist. Assoc. 448, 1231-1241] proposed a new method of boundary correction for kernel density estimation. Their technique is a kind of generalized reflection method involving reflecting a transformation of the data. In this paper, we present a modification to their estimator. We observe that this modification significantly improves the asymptotic bias and variance of their estimator.

Suggested Citation

  • Karunamuni, R.J. & Zhang, S., 2008. "Some improvements on a boundary corrected kernel density estimator," Statistics & Probability Letters, Elsevier, vol. 78(5), pages 499-507, April.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:5:p:499-507
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    References listed on IDEAS

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    1. Zhang, Shunpu, 2001. "Improvements on the kernel estimation in line transect sampling without the shoulder condition," Statistics & Probability Letters, Elsevier, vol. 53(3), pages 249-258, June.
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    Cited by:

    1. Gensler, André & Sick, Bernhard & Vogt, Stephan, 2018. "A review of uncertainty representations and metaverification of uncertainty assessment techniques for renewable energies," Renewable and Sustainable Energy Reviews, Elsevier, vol. 96(C), pages 352-379.
    2. Cattaneo, Matias D. & Jansson, Michael & Ma, Xinwei, 2024. "Local regression distribution estimators," Journal of Econometrics, Elsevier, vol. 240(2).
    3. Baszczyńska Aleksandra, 2016. "Kernel Estimation of Cumulative Distribution Function of a Random Variable with Bounded Support," Statistics in Transition New Series, Polish Statistical Association, vol. 17(3), pages 541-556, September.
    4. Joris Pinkse & Karl Schurter, 2019. "Estimation of Auction Models with Shape Restrictions," Papers 1912.07466, arXiv.org.
    5. Berry, Tyrus & Sauer, Timothy, 2017. "Density estimation on manifolds with boundary," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 1-17.
    6. Ma, Jun & Marmer, Vadim & Shneyerov, Artyom, 2019. "Inference for first-price auctions with Guerre, Perrigne, and Vuong’s estimator," Journal of Econometrics, Elsevier, vol. 211(2), pages 507-538.
    7. Gabrielli, M. Florencia & Willington, Manuel, 2023. "Estimating damages from bidding rings in first-price auctions," Economic Modelling, Elsevier, vol. 126(C).
    8. Taflanidis, Alexandros A. & Loukogeorgaki, Eva & Angelides, Demos C., 2013. "Offshore wind turbine risk quantification/evaluation under extreme environmental conditions," Reliability Engineering and System Safety, Elsevier, vol. 115(C), pages 19-32.
    9. Joris Pinkse & Karl Schurter, 2020. "Estimates of derivatives of (log) densities and related objects," Papers 2006.01328, arXiv.org.
    10. Tongyun Du & Henrik Vejre & Christian Fertner & Pengcheng Xiang, 2019. "Optimisation of Ecological Leisure Industrial Planning Based on Improved GIS-AHP: A Case Study in Shapingba District, Chongqing, China," Sustainability, MDPI, vol. 12(1), pages 1-29, December.
    11. Aleksandra Baszczyńska, 2016. "Kernel Estimation Of Cumulative Distribution Function Of A Random Variable With Bounded Support," Statistics in Transition New Series, Polish Statistical Association, vol. 17(3), pages 541-556, September.
    12. Aleksandra Baszczyńska, 2016. "Kernel Estimation of Cumulative Distribution Function of a Random Variable with Bounded Support," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 17(3), pages 541-556, September.
    13. Shunpu Zhang & Rohana Karunamuni, 2010. "Boundary performance of the beta kernel estimators," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(1), pages 81-104.
    14. Chaubey, Yogendra P. & Dewan, Isha & Li, Jun, 2011. "Smooth estimation of survival and density functions for a stationary associated process using Poisson weights," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 267-276, February.

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