Reducing Bias in Estimates for the Law of Crime Concentration
Reducing Bias in Estimates for the Law of Crime Concentration
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DOI：
10.1007/s10940-019-09404-1
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发表时间：
2019-12-01
影响因子：
3.6
通讯作者：
Short, Martin B.
中科院分区：
文献类型：
--
作者：
Mohler, George;Brantingham, P. Jeffrey;Short, Martin B.
犯罪集中定律指出，一个城市中一半的累积犯罪将发生在城市地理的大约4%之内。通过计算N个空间区域（街道段或网格单元）中每个区域的事件数量，然后基于计数计算参数，例如洛伦兹曲线或基尼指数上的点估计，来证明该定律。在这里，我们表明，在文献中常用的估计这些统计数据是有偏见的事件的数量很低（几千或更少）。我们的目标是显着减少偏差的法律犯罪concentration.MethodsBy建模犯罪计数作为一个负二项估计，我们展示了如何计算一个改进的估计的法律犯罪浓度在低事件计数，显着减少偏差。特别是，我们使用的泊松-伽马表示的负二项和计算浓度统计量通过积分的洛伦兹曲线和基尼指数的推断连续Gamma distribution.ResultsWe说明了泊松-伽马方法与合成数据沿着与凶杀案数据从芝加哥。我们表明，我们的估计显着减少偏差，并能够恢复真正的法律犯罪浓度只有几百events.ConclusionsThe泊松-伽马方法的浓度测量罕见的事件，不同规模的城市之间的浓度比较，并提高时间序列估计的犯罪浓度的应用。
ObjectivesThe law of crime concentration states that half of the cumulative crime in a city will occur within approximately 4% of the city's geography. The law is demonstrated by counting the number of incidents in each of N spatial areas (street segments or grid cells) and then computing a parameter based on the counts, such as a point estimate on the Lorenz curve or the Gini index. Here we show that estimators commonly used in the literature for these statistics are biased when the number of incidents is low (several thousand or less). Our objective is to significantly reduce bias in estimators for the law of crime concentration.MethodsBy modeling crime counts as a negative binomial, we show how to compute an improved estimate of the law of crime concentration at low event counts that significantly reduces bias. In particular, we use the Poisson-Gamma representation of the negative binomial and compute the concentration statistic via integrals for the Lorenz curve and Gini index of the inferred continuous Gamma distribution.ResultsWe illustrate the Poisson-Gamma method with synthetic data along with homicide data from Chicago. We show that our estimator significantly reduces bias and is able to recover the true law of crime concentration with only several hundred events.ConclusionsThe Poisson-Gamma method has applications to measuring the concentration of rare events, comparisons of concentration across cities of different sizes, and improving time series estimates of crime concentration.