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Estimation and Inference about Tail Features with Tail Censored Data

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Document pages: 41 pages

Abstract: This paper considers estimation and inference about tail features when theobservations beyond some threshold are censored. We first show that ignoringsuch tail censoring could lead to substantial bias and size distortion, even ifthe censored probability is tiny. Second, we propose a new maximum likelihoodestimator (MLE) based on the Pareto tail approximation and derive itsasymptotic properties. Third, we provide a small sample modification to the MLEby resorting to Extreme Value theory. The MLE with this modification deliversexcellent small sample performance, as shown by Monte Carlo simulations. Weillustrate its empirical relevance by estimating (i) the tail index and theextreme quantiles of the US individual earnings with the Current PopulationSurvey dataset and (ii) the tail index of the distribution of macroeconomicdisasters and the coefficient of risk aversion using the dataset collected byBarro and Urs{ú}a (2008). Our new empirical findings are substantiallydifferent from the existing literature.

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