The essential histogram
成果类型：
Article
署名作者：
Li, Housen; Munk, Axel; Sieling, Hannes; Walther, Guenther
署名单位：
University of Gottingen; Stanford University
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/asz081
发表日期：
2020
页码：
347364
关键词：
摘要：
The histogram is widely used as a simple, exploratory way of displaying data, but it is usually not clear how to choose the number and size of the bins. We construct a confidence set of distribution functions that optimally deal with the two main tasks of the histogram: estimating probabilities and detecting features such as increases and modes in the distribution. We define the essential histogram as the histogram in the confidence set with the fewest bins. Thus the essential histogram is the simplest visualization of the data that optimally achieves the main tasks of the histogram. The only assumption we make is that the data are independent and identically distributed. We provide a fast algorithm for computing the essential histogram and illustrate our method with examples.