Open Access
May 2018 Maximum likelihood estimation for the Fréchet distribution based on block maxima extracted from a time series
Axel Bücher, Johan Segers
Bernoulli 24(2): 1427-1462 (May 2018). DOI: 10.3150/16-BEJ903


The block maxima method in extreme-value analysis proceeds by fitting an extreme-value distribution to a sample of block maxima extracted from an observed stretch of a time series. The method is usually validated under two simplifying assumptions: the block maxima should be distributed exactly according to an extreme-value distribution and the sample of block maxima should be independent. Both assumptions are only approximately true. The present paper validates that the simplifying assumptions can in fact be safely made.

For general triangular arrays of block maxima attracted to the Fréchet distribution, consistency and asymptotic normality is established for the maximum likelihood estimator of the parameters of the limiting Fréchet distribution. The results are specialized to the common setting of block maxima extracted from a strictly stationary time series. The case where the underlying random variables are independent and identically distributed is further worked out in detail. The results are illustrated by theoretical examples and Monte Carlo simulations.


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Axel Bücher. Johan Segers. "Maximum likelihood estimation for the Fréchet distribution based on block maxima extracted from a time series." Bernoulli 24 (2) 1427 - 1462, May 2018.


Received: 1 March 2016; Revised: 1 September 2016; Published: May 2018
First available in Project Euclid: 21 September 2017

zbMATH: 06778369
MathSciNet: MR3706798
Digital Object Identifier: 10.3150/16-BEJ903

Keywords: asymptotic normality , block maxima method , heavy tails , maximum likelihood estimation , stationary time series , triangular arrays

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

Vol.24 • No. 2 • May 2018
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