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A Reliable Data-Based Bandwidth Selection Method for Kernel Density Estimation

S. J. Sheather and M. C. Jones
Journal of the Royal Statistical Society. Series B (Methodological)
Vol. 53, No. 3 (1991), pp. 683-690
Published by: Wiley for the Royal Statistical Society
Stable URL: http://www.jstor.org/stable/2345597
Page Count: 8
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A Reliable Data-Based Bandwidth Selection Method for Kernel Density Estimation
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Abstract

We present a new method for data-based selection of the bandwidth in kernel density estimation which has excellent properties. It improves on a recent procedure of Park and Marron (which itself is a good method) in various ways. First, the new method has superior theoretical performance; second, it also has a computational advantage; third, the new method has reliably good performance for smooth densities in simulations, performance that is second to none in the existing literature. These methods are based on choosing the bandwidth to (approximately) minimize good quality estimates of the mean integrated squared error. The key to the success of the current procedure is the reintroduction of a non-stochastic term which was previously omitted together with use of the bandwidth to reduce bias in estimation without inflating variance.

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