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Histogram-kernel Error and Its Application for Bin Width Selection in Histograms

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文摘 Histogram and kernel estimators are usually regarded as the two main classical data-based non- parametric tools to estimate the underlying density functions for some given data sets. In this paper we will integrate them and define a histogram-kernel error based on the integrated square error between histogram and binned kernel density estimator, and then exploit its asymptotic properties. Just as indicated in this paper, the histogram-kernel error only depends on the choice of bin width and the data for the given prior kernel densities. The asymptotic optimal bin width is derived by minimizing the mean histogram-kernel error. By comparing with Scott’s optimal bin width formula for a histogram, a new method is proposed to construct the data-based histogram without knowledge of the underlying density function. Monte Carlo study is used to verify the usefulness of our method for different kinds of density functions and sample sizes.
来源 Acta Mathematicae Applicatae Sinica-English Series ,2012,28(3):607-624 【核心库】
DOI 10.1007/s10255-007-7081-y
关键词 Histogram ; binned kernel density estimator ; bin width ; histogram-kernel error ; integrated square error
地址

1. Department of Mathematics, Graduate University of Chinese Academy of Sciences, Beijing, 100049  

2. College of Management, Graduate University of Chinese Academy of Sciences, Beijing, 100190

语种 英文
ISSN 0168-9673
学科 数学
基金 国家自然科学基金
文献收藏号 CSCD:4622838

参考文献 共 21 共2页

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