Univariate Tail Estimation : Lígia Henriques-Rodrigues
From Belle Taylor
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Name: Lígia Henriques-Rodrigues
Talk Title: Box-Cox estimation of parameters of extreme events
Abstract: The reduction of bias of the Hill estimator has been extensively addressed in the literature of extreme value theory. Several techniques have been used to achieve such reduction of bias, either by removing the main component of the bias of the Hill estimator of the extreme value index (EVI) or by constructing new estimators based on generalized means or norms that generalize the Hill estimator. In statistical literature the Box-Cox transformations are used to make the data more suitable for statistical analysis. Using the regular variation theory, Teugles and Vanrolen, in 2004, studied the effect of the Box-Cox transformations in the speed of convergence of the second order condition and proposed the Box-Cox Hill estimator. In this work we are going to address the choice and estimation of the power and shift parameters of the Box-Cox transformation, not only for the EVI-estimation, but also for the estimation of other parameters of extreme events. We shall prove the consistency and asymptotic normality of these estimators and their performance for finite samples is illustrated through a small-scale Monte-Carlo simulation study.
This talk is a contributed talk at EVA 2021.