On Asymptotic Normality of Hill's Estimator for the Exponent of Regular Variation

Abstract

It is shown that Hill's estimator (1975) for the exponent of regular variation is asymptotically normal if the number $k_n$ of extreme order statistics used to construct it tends to infinity appropriately with the sample size $n.$ As our main result, we derive a general condition which can be used to determine the optimal $k_n$ explicitly, provided that some prior knowledge is available on the underlying distribution function with regularly varying upper tail. This condition is simplified under appropriate assumptions and then applied to several examples.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 214 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.