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INTERPOLATING THE LORENZ CURVE: METHODS TO PRESERVE SHAPE AND REMAIN CONSISTENT WITH THE CONCENTRATION CURVES FOR COMPONENTS

机译:插入LORENZ曲线:保持形状并与组件的浓度曲线保持一致的方法

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摘要

C~1-class interpolation methods that preserve monotonicity and convexity and are thus suitable for the estimation of the Lorenz curve from grouped data are not widely known. Instead, parametric models are usually applied for such estimation. Parametric models, however, have difficulty in accurately approximating every part of income/expenditure distributions. This paper proposes two types of C~1-class shape-preserving interpolation methods. One is a piecewise rational polynomial interpolation (proposed independently by Stineman and Delbourgo) that enables consistent interpolation of the concentration curves for income/expenditure components, attaining approximately the same accuracy as that of the existing methods when applied to decile-grouped data or to more detailed aggregation. Another is a Hybrid interpolation that employs pieces of curves derived from parametric models on end intervals. Empirical comparisons show that the Hybrid interpolation (with the assistance of parametric models for class-boundary estimation) outperforms the existing methods even when applied to quintile-grouped data without class boundaries.
机译:保留单调性和凸性并因此适合从分组数据估计Lorenz曲线的C-1类插值方法尚未广为人知。相反,通常将参数模型应用于这种估计。但是,参数模型很难准确估计收入/支出分布的每个部分。提出了两种C-1类保形插值方法。一种是分段有理多项式插值法(由Stineman和Delbourgo独立提出),可以对收入/支出成分的集中曲线进行一致的插值,当应用于十进制分组数据或更多时,其精度与现有方法大致相同。详细的汇总。另一个是混合插值,它采用从参数模型得出的末端区间上的曲线。经验比较表明,即使应用于没有类别边界的五分位数分组数据,混合插值(借助用于类边界估计的参数模型)也优于现有方法。

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