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Nonparametric kernel density estimation for general grouped data

Author

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  • Miguel Reyes
  • Mario Francisco-Fernández
  • Ricardo Cao

Abstract

Interval-grouped data are defined, in general, when the event of interest cannot be directly observed and it is only known to have been occurred within an interval. In this framework, a nonparametric kernel density estimator is proposed and studied. The approach is based on the classical Parzen--Rosenblatt estimator and on the generalisation of the binned kernel density estimator. The asymptotic bias and variance of the proposed estimator are derived under usual assumptions, and the effect of using non-equally spaced grouped data is analysed. Additionally, a plug-in bandwidth selector is proposed. Through a comprehensive simulation study, the behaviour of both the estimator and the plug-in bandwidth selector considering different scenarios of data grouping is shown. An application to real data confirms the simulation results, revealing the good performance of the estimator whenever data are not heavily grouped.

Suggested Citation

  • Miguel Reyes & Mario Francisco-Fernández & Ricardo Cao, 2016. "Nonparametric kernel density estimation for general grouped data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 235-249, June.
    • Handle: RePEc:taf:gnstxx:v:28:y:2016:i:2:p:235-249
    DOI: 10.1080/10485252.2016.1163348
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    Cited by:

    1. Emmanuel Hagenimana & Song Lixin & Patrick Kandege, 2018. "Study of nonparametric estimation details of instant system availability average," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 9(2), pages 467-481, April.
    2. Lee, Ji Hyung & Sasaki, Yuya & Toda, Alexis Akira & Wang, Yulong, 2024. "Tuning parameter-free nonparametric density estimation from tabulated summary data," Journal of Econometrics, Elsevier, vol. 238(1).
    3. Miguel Reyes & Mario Francisco-Fernández & Ricardo Cao, 2017. "Bandwidth selection in kernel density estimation for interval-grouped data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 527-545, September.

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