Inference on heavy tails from dependent data

Statistics of extremes has been well developed for the case of independent and identically distributed (i.i.d.) observations. In a growing number of applications, however, the data appears dependent and heavy{tailed. We deal with problems of tail index and extreme quantile estimation from a sample of dependent random variables. Consistency and asymptotic normality of the corresponding estimators are established under mild mixing conditions. The accuracy of estimation is shown to be of the same order as if the data were independent. We suggest an approach to bias reduction. Besides limit theorems, we present a procedure of practical estimation.

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