 Locally optimal window widths for kernel density estimation with large samplesWilliam R. Schucany Statistics & Probability Letters, 1989, vol. 7, issue 5, 401-405 Abstract: The smoothing parameter or window width for a kernel estimator of a probability density at a point has been previously specified to minimize either asymptotic mean square error or asymptotic mean absolute error. In this note the ratio of these two widths is shown to be a constant for all kernels and density functions that satisfy the usual smoothness conditions. The fact that this ratio equals 0.985 supports recent comment that in this context these two error criteria do not yield large-sample results that differ by any meaningful amount. Isolated points at which the dominant term of the conventional bias expansion vanishes are examined. Consideration of additional terms and continuity leads to the conclusion that bias is adequately modeled by a multiple of a single rate in all large but finite sample sizes. In practice, for instance, at inflection points with a second-order kernel the abrupt change in exponent from 1/5 to 1/9 is not necessarily a good representation. Keywords: bandwidth; bias; mean; absolute; error; mean; square; error; smoothing; parameter (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:7:y:1989:i:5:p:401-405 Ordering information: This journal article can be ordered from Access Statistics for this article Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul More articles in Statistics & Probability Letters from Elsevier |
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