WebApr 7, 2011 · Title: Once more on comparison of tail index estimators. Authors: Vygantas Paulauskas, Marijus Vaičiulis. Download PDF Abstract: We consider heavy-tailed … WebWe compare various estimators for the index of distribution functions with regularly varying tails by calculating their asymptotic mean squared errors after choosing the optimal …

A MODIFICATION OF HILL’S TAIL INDEX ESTIMATOR

WebIn the paper, we propose a new class of functions which is used to construct tail index estimators. Functions from this new class are non-monotone in general, but they are the product of two monotone functions: the power function and the logarithmic function, which play essential role in the classical Hill estimator. WebJun 6, 2016 · The tail index as a measure of tail thickness provides information that is not captured by standard volatility measures. It may however change over time. Currently available procedures for detecting those changes for dependent data (e.g., Quintos et al ., 2001) are all based on comparing Hill ( 1975) estimates from different subsamples. bring brandon home

ESTIMATION OF RISK MEASURES FROM HEAVY TAILED DISTRIBUTIONS

Webthe number of tail data that have to be used in the estimation of the tail index. The tail index is the shape parameter of these heavy tailed distributions. The most popular estimator for the tail index of heavy tailed distributions is the Hill (1975) estimator. This estimator necessitates a choice of the number of order statistics utilized in ... WebKey words: Bias, censored likelihood function, Hill estimator, second order regular variation, tail index. 1. Introduction In order to estimate high quantiles or extreme tail probabilities of an unknown distribution function, we have to estimate beyond the observations, so extra assumptions on the underlying distribution function are needed. bring brands to life