Maximum likelihood estimation for the Fréchet distribution based on block maxima extracted from a time series
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Date
2015
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Abstract
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 Frechet distribution,
consistency and asymptotic normality is established for the maximum likelihood
estimator of the parameters of the limiting Frechet 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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Keywords
block maxima method, stationary time series, triangular arrays, heavy tails, asymptotic normality, maximum likelihood estimation