Practical Kolmogorov–Smirnov Testing by Minimum Distance Applied to Measure Top Income Shares in Korea
研究了一种用最小距离估计参数后进行Kolmogorov–Smirnov拟合优度检验的方法，并将其应用于韩国2007-2012年所得税数据，发现帕累托尾假设在估计前0.1%以上收入份额时成立，但在估计前1%或0.5%时被拒绝。
<p>We study Kolmogorov–Smirnov goodness-of-fit tests for evaluating distributional hypotheses where unknown parameters need to be fitted. Following the work of Pollard (1980), our approach uses a Cramér–von Mises minimum distance estimator for parameter estimation. The asymptotic null distribution of the resulting test statistic is represented by invariance principle arguments as a functional of a Brownian bridge in a simple regression format for which asymptotic critical values are readily delivered by simulations. Asymptotic power is examined under fixed and local alternatives and finite sample performance of the test is evaluated in simulations. The test is applied to measure top income shares using Korean income tax return data over 2007–2012. When the data relate to estimating the upper 0.1% or higher income shares, the conventional assumption of a Pareto tail distribution cannot be rejected. But the Pareto tail hypothesis is rejected for estimating the top 1.0% or 0.5% income shares at the 5% significance level. A supplement containing proofs and data descriptions is available online.</p>