  Modern statistical analyses often encounter datasets with massive sizes and
heavy-tailed distributions. For datasets with massive sizes, traditional
estimation methods can hardly be used to estimate the extreme value index
directly. To address the issue, we propose here a subsampling-based method.
Specifically, multiple subsamples are drawn from the whole dataset by using the
technique of simple random subsampling with replacement. Based on each
subsample, an approximate maximum likelihood estimator can be computed. The
resulting estimators are then averaged to form a more accurate one. Under
appropriate regularity conditions, we show theoretically that the proposed
estimator is consistent and asymptotically normal. With the help of the
estimated extreme value index, we can estimate high-level quantiles and tail
probabilities of a heavy-tailed random variable consistently. Extensive
simulation experiments are provided to demonstrate the promising performance of
our method. A real data analysis is also presented for illustration purpose.
