论文标题
一类新的综合指标：惩罚能力意味着
A new class of composite indicators: the penalized power means
论文作者
论文摘要
在本文中，我们提出了一种新的聚合方法，用于构建基于权力平均值的惩罚的综合指标。这种方法的基础想法包括将力量平均值乘以一个因素，该因素考虑了指标之间的水平异质性，目的是用更大的异质性惩罚单位。为了衡量这种异质性，我们通过其功率平均值扩展了归一化指标的向量，我们计算了通过适当的盒子cox函数转换的缩放标准化指标的方差，并且我们测量了异质性作为通过Box-Cox函数的该方差的计数器图像。最终的惩罚因素可以解释为我们以其功率平均值代替归一化指标的向量的相对误差或信息丢失。这种惩罚方法具有完全数据驱动的优势，并与权力平均方法的基本原理相一致，即信息原则的最小损失，也可以允许更精致的排名。命令的惩罚力量意味着与Mazziotta Pareto指数相吻合。
In this paper we propose a new aggregation method for constructing composite indicators that is based on a penalization of the power means. The idea underlying this approach consists in multiplying the power mean by a factor that takes into account for the horizontal heterogeneity among indicators with the aim of penalizing the units with larger heterogeneity. In order to measure this heterogeneity, we scale the vector of normalized indicators by their power means, we compute the variance of the scaled normalized indicators transformed by means of the appropriate Box-Cox function, and we measure the heterogeneity as the counter image of this variance through the Box-Cox function. The resulting penalization factor can be interpreted as the relative error, or the loss of information, that we obtain substituting the vector of the normalized indicators with their power mean. This penalization approach has the advantage to be fully data-driven and to be coherent with the same principle underlying the power mean approach, that is the minimum loss of information principle as well as to allow for a more refined rankings. The penalized power mean of order one coincides with the Mazziotta Pareto Index.
