Variations on the Histogram
Variations on the Histogram
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DOI：
10.1198/jcgs.2009.0002
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发表时间：
2009-03-01
影响因子：
2.4
通讯作者：
Mallows, Colin
中科院分区：
文献类型：
--
作者：
Denby, Lorraine;Mallows, Colin
在构造直方图时，通常会使所有条形图的宽度相同。也可以选择使它们都具有相同的面积。这两个选项具有互补的优点和缺点;等宽直方图在高密度区域中过平滑，并且在识别尖峰方面很差;等面积直方图在低密度区域中过平滑，因此不能识别离群值。我们描述了一个折衷的方法，避免了这两个缺陷。我们把直方图看作是一种探索性的工具，而不是密度的估计。我们认为，依赖于积分均方误差的渐近性会导致不适当的建议，选择面元宽度。数据集和R代码可在网上补充。
When constructing a histogram, it is common to make all bars the same width. One could also choose to make them all have the same area. These two options have complementary strengths and weaknesses; the equal-width histogram oversmooths in regions of high density, and is poor at identifying sharp peaks; the equal-area histogram oversmooths in regions of low density, and so does not identify outliers. We describe a compromise approach which avoids both of these defects. We regard the histogram as an exploratory device, rather than as an estimate of a density. We argue that relying on the asymptotics of integrated mean squared error leads to inappropriate recommendations for choosing bin-widths.Datasets and R codes are available in the online supplements.