A note on kernel polygons

Authors: Lin, Chien-Tai; Wu, Jyh-Shyang; Yen, Chia-Hung

Source: Biometrika, Volume 93, Number 1, March 2006 , pp. 228-234(7)

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Abstract:

Jones (1989) has pointed out that piecewise linear interpolated kernel density estimators on a sufficiently fine grid can be visually indistinguishable from the true density. A simple device, the kernel polygon, is proposed for eliminating the evaluation of the normalisation constant of the estimator while retaining its property of being a density function as well as providing practical advantages. The class of uniform and linear kernels of the kernel polygons is given. Finally, we present a simulation study and a real data example in which we compare bandwidth selectors for the kernel polygons.

Keywords: Edge frequency polygon; Frequency polygon; Integrated mean squared error; Kernel density estimator; Smoothing

Document Type: Research article

DOI: http://dx.doi.org/10.1093/biomet/93.1.228

Publication date: 2006-03-01