从分组收入数据中获得更好的估计：插值CDF和均值匹配
Better estimates from binned income data: Interpolated CDFs and mean-matching
摘要：
研究人员经常从摘要中估计收入统计数据，这些摘要报告了收入箱中的收入数量，如0 - 10，000美元，10，001 - 20，000美元，...，20万+。一些分析师将收入分配给中间点，但这将收入视为离散的。其他分析师拟合连续参数分布，但分布可能拟合得不好。我们拟合非参数连续分布，通过插值累积分布函数（CDF）来完美地再现bin计数。我们还展示了如何中点和插值CDF可以被约束，以重现收入的平均值时，它是已知的。我们比较了这些方法在估计美国所有3,221个县的基尼系数时的准确性。拟合参数分布非常慢。拟合插值CDF要快得多，而且精度也稍高。如果约束匹配已知均值，插值CDF和中点都能提供更好的估计值。我们已经在R的binsmooth包中实现了插值CDF。我们已经在Stata的rpme命令中实现了中点方法。这两种实现都可以被限制为匹配已知均值。
英文摘要：
Researchers often estimate income statistics from summaries that report the number of incomes in bins such as \$0-10,000, \$10,001-20,000,...,\$200,000+. Some analysts assign incomes to bin midpoints, but this treats income as discrete. Other analysts fit a continuous parametric distribution, but the distribution may not fit well. We fit nonparametric continuous distributions that reproduce the bin counts perfectly by interpolating the cumulative distribution function (CDF). We also show how both midpoints and interpolated CDFs can be constrained to reproduce the mean of income when it is known. We compare the methods' accuracy in estimating the Gini coefficients of all 3,221 US counties. Fitting parametric distributions is very slow. Fitting interpolated CDFs is much faster and slightly more accurate. Both interpolated CDFs and midpoints give dramatically better estimates if constrained to match a known mean. We have implemented interpolated CDFs in the binsmooth package for R. We have implemented the midpoint method in the rpme command for Stata. Both implementations can be constrained to match a known mean.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
