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Optimal Bandwidth Selection for Kernel Density Functionals Estimation

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  • Su Chen

Abstract

The choice of bandwidth is crucial to the kernel density estimation (KDE) and kernel based regression. Various bandwidth selection methods for KDE and local least square regression have been developed in the past decade. It has been known that scale and location parameters are proportional to density functionals with appropriate choice of and furthermore equality of scale and location tests can be transformed to comparisons of the density functionals among populations. can be estimated nonparametrically via kernel density functionals estimation (KDFE). However, the optimal bandwidth selection for KDFE of has not been examined. We propose a method to select the optimal bandwidth for the KDFE. The idea underlying this method is to search for the optimal bandwidth by minimizing the mean square error (MSE) of the KDFE. Two main practical bandwidth selection techniques for the KDFE of are provided: Normal scale bandwidth selection (namely, “Rule of Thumb”) and direct plug-in bandwidth selection. Simulation studies display that our proposed bandwidth selection methods are superior to existing density estimation bandwidth selection methods in estimating density functionals.

Suggested Citation

  • Su Chen, 2015. "Optimal Bandwidth Selection for Kernel Density Functionals Estimation," Journal of Probability and Statistics, Hindawi, vol. 2015, pages 1-21, August.
    • Handle: RePEc:hin:jnljps:242683
    DOI: 10.1155/2015/242683
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    Cited by:

    1. Yi Jin & Yulin He & Defa Huang, 2021. "An Improved Variable Kernel Density Estimator Based on L 2 Regularization," Mathematics, MDPI, vol. 9(16), pages 1-12, August.
    2. Ye Tian & Yasunari Yokota, 2019. "Estimating the Major Cluster by Mean-Shift with Updating Kernel," Mathematics, MDPI, vol. 7(9), pages 1-25, August.
    3. Shahid Latif & Slobodan P. Simonovic, 2023. "Trivariate Probabilistic Assessments of the Compound Flooding Events Using the 3-D Fully Nested Archimedean (FNA) Copula in the Semiparametric Distribution Setting," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 37(4), pages 1641-1693, March.
    4. Moawia Alghalith, 2022. "Methods in Econophysics: Estimating the Probability Density and Volatility," Papers 2301.10178, arXiv.org.
    5. Shahid Latif & Slobodan P. Simonovic, 2022. "Nonparametric Approach to Copula Estimation in Compounding The Joint Impact of Storm Surge and Rainfall Events in Coastal Flood Analysis," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(14), pages 5599-5632, November.
    6. John Paolo Rosales Rivera, 2022. "A nonparametric approach to understanding poverty in the Philippines: Evidence from the Family Income and Expenditure Survey," Poverty & Public Policy, John Wiley & Sons, vol. 14(3), pages 242-267, September.

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