When interval-grouped data are available, the classical Parzen–Rosenblatt kernel density estimator has to be modified to get a computable and useful approach in this context. The new nonparametric grouped data estimator needs of the choice of a smoothing parameter. In this paper, two different bandwidth selectors for this estimator are analyzed. A plug-in bandwidth selector is proposed and its relative rate of convergence obtained. Additionally, a bootstrap algorithm to select the bandwidth in this framework is designed. This method is easy to implement and does not require Monte Carlo. Both proposals are compared through simulations in different scenarios. It is observed that when the sample size is medium or large and grouping is not heavy, both bandwidth selection methods have a similar and good performance. However, when the sample size is large and under heavy grouping scenarios, the bootstrap bandwidth selector leads to better results.
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This research has been partially supported by the Spanish Ministry of Science and Innovation, Grants MTM2011-22392 and MTM2014-52876-R, and Xunta de Galicia Grant CN2012/130. The authors thank two anonymous referees for numerous useful comments that significantly improved this article.
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Reyes, M., Francisco-Fernández, M. & Cao, R. Bandwidth selection in kernel density estimation for interval-grouped data. TEST 26, 527–545 (2017). https://doi.org/10.1007/s11749-017-0523-9
- Smoothing parameter selection
- Plug-in bandwidth
- Bootstrap bandwidth selector
- Interval data
Mathematics Subject Classification