Local Bandwidth Selection for Density Estimation

Lori A. Thombs and Simon J. Sheather
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Lori A. Thombs: University of South Carolina
Simon J. Sheather: University of New South Wales

A chapter in Computing Science and Statistics, 1992, pp 111-116 from Springer

Abstract: Abstract The problem of choosing a local value of the bandwidth h for a kernel density estimate is considered. Estimates of the density f at a given point are needed in the estimation of the asymptotic standard error or sample quantiles and in some kernel regression estimators based on random design points. The value of the bandwidth that minimizes the asymptotic MSE of the kernel estimate at the point x involves both f(x) and f″(x). In this paper we show that the “solve-the-equation” bandwidth selection method of Sheather (1986) produces an estimate of the asymptotically optimal h which has relative rate of convergence of n-2/9. We also show how higher order kernel estimates of f″ can be used to improve this rate to n-2/5. How much reliance can be placed on these theoretical results is investigated through a simulation study which compares the performance of a number of different selection methods

Keywords: Kernel Density Estimate; Cauchy Distribution; Bandwidth Selection; Asymptotic Standard Error; Sample Quantile (search for similar items in EconPapers)
Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-2856-1_14

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DOI: 10.1007/978-1-4612-2856-1_14

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