直方图理论与最优直方图制作

直方图是一种最为常见的密度估计和数据分析工具. 在直方图理论和制作过程中, 组距的选择和边界点的确定尤为重要. 然而, 许多学者对这两个参数的选择仍然采用经验的方法, 甚至现在大多数统计软件在确定直方图分组数时也是默认采用粗略的计算公式. 本文主要介绍直方图理论和最优直方图制作的最新研究成果, 强调面向样本的最优直方图制作方法.

Histogram Theories and Optimal Histogram Construction Algorithms

Histogram is the most widely used density estimator and data analysis tool. It is completely determined by two parameters: the bin width and one of the bin edges. However, many professional statisticians have no really definitive answers and simply give some intuitive advises when face to choose these two parameters. Even most statistical packages use the rules of thumbs for selecting the number of bins as a default. In this paper, we will present the histogram theories and optimal histogram construction algorithms that have been recently proposed. The methods of how to construct the data-based histograms are theemphasis of this paper.