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Biometrika 2006 93(1):228-234; doi:10.1093/biomet/93.1.228
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© 2006 Biometrika Trust

Miscellanea

A note on kernel polygons

Chien-Tai Lin, Jyh-Shyang Wu and Chia-Hung Yen

Department of Mathematics, Tamkang University, Tamsui 251 Taiwan chien{at}math.tku.edu.tw, jswu{at}math.tku.edu.tw, yenjh{at}center.fjtc.edu.tw

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.

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

Received January 2005. Revised July 2005.


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