尾截尾数据下尾特征的估计与推断
Estimation and Inference about Tail Features with Tail Censored Data
摘要：
本文研究了当超过一定阈值的观测值被删失时尾部特征的估计和推断。我们首先表明，忽略这种尾部删失可能会导致大量的偏见和大小失真，即使删失概率很小。其次，我们提出了一个新的极大似然估计（MLE）的基础上的Pareto尾近似，并推导出其渐近性质。第三，我们提供了一个小样本的修改MLE诉诸极值理论。通过蒙特卡罗模拟，这种修改的MLE提供了出色的小样本性能。我们通过估计（i）使用当前人口调查数据集的美国个人收入的尾部指数和极端分位数以及（ii）使用Barro和Urs{ú}a（2008）收集的数据集的宏观经济灾难分布的尾部指数和风险规避系数来说明其经验相关性。我们新的实证研究结果与现有文献有很大不同。
英文摘要：
This paper considers estimation and inference about tail features when the observations beyond some threshold are censored. We first show that ignoring such tail censoring could lead to substantial bias and size distortion, even if the censored probability is tiny. Second, we propose a new maximum likelihood estimator (MLE) based on the Pareto tail approximation and derive its asymptotic properties. Third, we provide a small sample modification to the MLE by resorting to Extreme Value theory. The MLE with this modification delivers excellent small sample performance, as shown by Monte Carlo simulations. We illustrate its empirical relevance by estimating (i) the tail index and the extreme quantiles of the US individual earnings with the Current Population Survey dataset and (ii) the tail index of the distribution of macroeconomic disasters and the coefficient of risk aversion using the dataset collected by Barro and Urs{ú}a (2008). Our new empirical findings are substantially different from the existing literature.
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