Maximum likelihood estimation for the Fréchet distribution based on block maxima extracted from a time series

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 according to an extreme-value distribution and the sample of block maxima should be independent. Both assumptions are only approximately true. For general triangular arrays of block maxima attracted to the Fr\'echet distribution, consistency and asymptotic normality is established for the maximum likelihood estimator of the parameters of the limiting Fr\'echet distribution. The results are specialized to the 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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Document type	Article de périodique (Journal article) – Article de recherche
Access type	Accès libre
Publication date	2018
Language	Anglais
Journal information	"Bernoulli : a journal of mathematical statistics and probability" - Vol. 24, no. 2, p. 1427-1462 (2018)
Peer reviewed	yes
Publisher	International Statistical Institute ((Netherlands) The Hague)
issn	1350-7265
e-issn	1573-9759
Publication status	Publié
Affiliation	UCL - SSH/LIDAM/ISBA - Institut de Statistique, Biostatistique et Sciences Actuarielles
Keywords	block maxima method ; maximum likelihood estimation ; asymptotic normality ; heavy tails ; triangular arrays ; stationary time series
Links	https://arxiv.org/abs/1511.07613v2 http://hdl.handle.net/2078.1/180480[Handle] https://doi.org/10.3150/16-BEJ903[DOI]

See also
	[boreal:168137]	Maximum likelihood estimation for the Fréchet distribution based on block maxima extracted from a time series