Data-Based Choice of Histogram Bin Width
Data-Based Choice of Histogram Bin Width
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DOI：
10.1080/00031305.1997.10473591
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发表时间：
1997-02
期刊：
影响因子：
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通讯作者：
M. Wand
中科院分区：
文献类型：
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作者：
M. Wand
摘要 直方图最重要的参数是箱宽，因为它控制着相对于真实分布而言细节过多（“平滑不足”）或细节过少（“过度平滑”）的图片之间的权衡。尽管如此重要，但令人惊讶的是，对“最佳”箱宽度估计的研究却很少。大多数常见统计包中的默认箱宽度（至少对于大样本而言）与最佳箱宽度相差甚远。例如，Scott 提出的规则可以提高直方图的大样本性能，但其本身并不一致。在本文中，我们将 Scott 的 bin 宽度规则扩展到那些能够达到 L 2 最优 bin 宽度的 n 根收敛率的规则，从而为其使用提供了坚实的科学依据。此外，所提出的规则计算简单、容易且快速，并且在模拟中表现良好。
Abstract The most important parameter of a histogram is the bin width because it controls the tradeoff between presenting a picture with too much detail (“undersmoothing”) or too little detail (“oversmoothing”) with respect to the true distribution. Despite this importance there has been surprisingly little research into estimation of the “optimal” bin width. Default bin widths in most common statistical packages are, at least for large samples, quite far from the optimal bin width. Rules proposed by, for example, Scott lead to better large sample performance of the histogram, but are not consistent themselves. In this paper we extend the bin width rules of Scott to those that achieve root-n rates of convergence to the L 2-optimal bin width, thereby providing firm scientific justification for their use. Moreover, the proposed rules are simple, easy and fast to compute, and perform well in simulations.