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A note on the asymptotic normality of the ET method for extreme quantile estimation

✍ Scribed by Jean Diebolt; Stéphane Girard

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
224 KB
Volume
62
Category
Article
ISSN
0167-7152

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✦ Synopsis

In this note, we establish the asymptotic distribution of the exponential tail estimator of extreme quantiles. We give su cient conditions for the asymptotic normality and provide some illustrating examples.

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We consider a stationary time series [X t ] given by X t = k= & k Z t&k , where [Z t ] is a strictly stationary martingale difference white noise. Under assumptions that the spectral density f (\*) of [X t ] is squared integrable and m { |k| m 2 k Ä 0 for some {>1Â2, the asymptotic normality of the