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敏感性分析中的渐近可分性AI 解读

Summary In an observational study in which each treated subject is matched to several untreated controls by using observed pretreatment covariates, a sensitivity analysis asks how hidden biases due to unobserved covariates might alter the conclusions. The bounds required for a sensitivity analysis are the solution to an optimization problem. In general, this optimization problem is not separable, in the sense that one cannot find the needed optimum by performing a separate…

分组数据估计的基尼及相关不平等指数界限的大样本理论AI 解读

The joint asymptotic distribution of the upper and lower bounds for the Gini index derived by Gastwirth for grouped data are obtained. From them a conservative asymptotically distribution-free confidence interval for the population Gini index is presented. The methods also yield similar results for other indices of inequality (e.g., Theil's and Atkinson's).

短评：评 Vinod《黑人与白人经济距离的测量》AI 解读

Vinod ( 1 985) recently noted that there was room for additional measures to compare two distribution funcLl [F(,x-) G(x)] day tions and introduced a new concept-economic advantage-that could be defined over either a small range of the income curve or the whole range (the + 1 G ) ) 1 F ) ] d (2) overall economic advantage; OEA). He then developed a statistical methodology for estimating these measures which from ParZen (1960, p. 21 1) is and applied them to U.S. income data.…

若干收入不平等测度的大样本理论AI 解读

THE MEASUREMENT of economic inequality is a timely and important topic. Often the Gini index or the entire Lorenz curve is used; however, the relative mean deviation (or Pietra ratio) has been used by Schutz [9] and Budd [1] to study United States data. Eltet6 and Frigyes [2] developed new measures to aid in their analysis of Hungary's income distribution, and Kondor [6] has shown that these new indices are related to the relative mean deviation. In order to draw valid…

基于分组数据的洛伦兹曲线与基尼指数插值AI 解读

ECONOMISTS OFTEN SUMMARIZE the income distribution by the Lorenz curve and Gini index. A variety of parametric methods (e.g., [1 and 8]) have been developed to estimate these measures from the grouped income data governments provide (e.g., [3 and 12]). Previously, one of the authors developed a distribution-free approach [5] which yielded accurate bounds on the Gini index. While analogous bounds on the Lorenz curve can be obtained [5 and 10], the resulting curve is not…

利用分组数据界定分布矩AI 解读

This article derives bounds on a wide class of moments of the underlying distribution from data grouped in intervals when the mean of each group is given. The extremal distributions are constructed yielding the upper and lower bounds to moments of the form ∫h(x)dF(x), where h(x) is convex and F(x) is concave. To illustrate the results, bounds on the variance and Gini index are presented for two theoretical distributions.