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A variable bandwidth selector in multivariate kernel density estimation

Author

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  • Wu, Tiee-Jian
  • Chen, Ching-Fu
  • Chen, Huang-Yu

Abstract

Based on a random sample of size n from an unknown d-dimensional density f, the problem of selecting the variable (or adaptive) bandwidth in kernel estimation of f is investigated. The common strategy is to express the variable bandwidth at each observation as the product of a local bandwidth factor and a global smoothing parameter. For selecting the local bandwidth factor a method based on cluster analysis is proposed. This method is direct and intuitively appealing. For selecting the global smoothing parameter a method that is an adaptation of the frequency domain approach of selecting the fixed bandwidth in Wu and Tsai [2004. Root n bandwidths selectors in multivariate kernel density estimation. Probab. Theory Related Fields 129, 537-558] is used. For d=1 and 2, extensive simulation studies have been done to compare the performance of our selector with the selectors of Abramson [1982. On bandwidth variation in kernel estimates--a square root law. Ann. Statist. 10, 1217-1223] and Sain and Scott [1996. On locally adaptive density estimation. J. Amer. Statist. Assoc. 91, 1525-1534] and Sain [2002. Multivariate locally adaptive density estimation. Comput. Statist. Data Anal. 39, 165-186], and the excellent performance of our selector at practical sample sizes is clearly demonstrated.

Suggested Citation

  • Wu, Tiee-Jian & Chen, Ching-Fu & Chen, Huang-Yu, 2007. "A variable bandwidth selector in multivariate kernel density estimation," Statistics & Probability Letters, Elsevier, vol. 77(4), pages 462-467, February.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:4:p:462-467
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    References listed on IDEAS

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    1. M. Jones & I. McKay & T. Hu, 1994. "Variable location and scale kernel density estimation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(3), pages 521-535, September.
    2. Sain, Stephan R., 2002. "Multivariate locally adaptive density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 39(2), pages 165-186, April.
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    Cited by:

    1. Catalina Bolance & Montserrat Guillen & David Pitt, 2014. "Non-parametric Models for Univariate Claim Severity Distributions - an approach using R," Working Papers 2014-01, Universitat de Barcelona, UB Riskcenter.
    2. Xijian Hu & Yaori Lu & Huiguo Zhang & Haijun Jiang & Qingdong Shi, 2021. "Selection of the Bandwidth Matrix in Spatial Varying Coefficient Models to Detect Anisotropic Regression Relationships," Mathematics, MDPI, vol. 9(18), pages 1-14, September.
    3. David Pitt & Montserrat Guillén, 2010. "An introduction to parametric and non-parametric models for bivariate positive insurance claim severity distributions," Working Papers XREAP2010-03, Xarxa de Referència en Economia Aplicada (XREAP), revised Mar 2010.
    4. David Pitt & Montserrat Guillen & Catalina Bolancé, 2011. "Estimation of Parametric and Nonparametric Models for Univariate Claim Severity Distributions - an approach using R," Working Papers XREAP2011-06, Xarxa de Referència en Economia Aplicada (XREAP), revised Jun 2011.
    5. Adriano Z. Zambom & Ronaldo Dias, 2013. "A Review of Kernel Density Estimation with Applications to Econometrics," International Econometric Review (IER), Econometric Research Association, vol. 5(1), pages 20-42, April.
    6. 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.
    7. Madan Mohan Rout & Josodhir Das & Kamal, 2018. "Probabilistic seismic hazard for Himalayan region using kernel estimation method (zone-free method)," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 93(2), pages 967-985, September.
    8. Bolancé, Catalina & Guillén, Montserrat & Nielsen, Jens Perch, 2008. "Inverse beta transformation in kernel density estimation," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1757-1764, September.
    9. Mohsen Arefi & Reinhard Viertl & S. Taheri, 2012. "Fuzzy density estimation," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(1), pages 5-22, January.

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