ABSTRACT The so-called growth incidence curve (GIC) is a popular way to evaluate the distributional pattern of economic growth and pro-poorness of growth in development economics. The log-transformation of the the GIC is related to the sum of empirical quantile processes which allows for constructions of simultaneous confidence bands for the GIC. However, standard constructions of these bands tend to be too wide at the extreme points 0 and 1 because the estimator of the quantile function can be very volatile at the extreme points. In order to construct simultaneous confidence bands which are narrower at the ends, we consider the convergence of quantile processes with weight functions. In particular, we investigate the asymptotic convergence under specific weighted sup-norm metrics and compare different kinds of qualified weight functions. This implies simultaneous confidence bands that are narrower at the boundaries 0 and 1. We show in simulations that these bands have a more regular shape. Finally, we evaluate real data from Uganda with the improved confidence bands.

中文翻译：

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加权超范指标中生长发生率曲线的同时置信带

摘要 所谓的增长关联曲线 (GIC) 是评估发展经济学中经济增长的分配模式和有利于穷人的增长的一种流行方法。GIC 的对数转换与经验分位数过程的总和有关，这允许构建 GIC 的同时置信区间。然而，这些带的标准构造在极值点 0 和 1 处往往太宽，因为分位数函数的估计量在极值点可能非常不稳定。为了构建两端较窄的同时置信带，我们考虑分位数过程与权重函数的收敛。特别是，我们研究了特定加权超范数下的渐近收敛性，并比较了不同类型的合格权重函数。这意味着同时置信带在边界 0 和 1 处更窄。我们在模拟中显示这些带具有更规则的形状。最后，我们使用改进的置信区间评估来自乌干达的真实数据。