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Regular version of the site

Article

A note on the bootstrap method for testing the existence of finite moments

Statistica. 2014. Vol. 74. No. 4. P. 447-453.
Fedotenkov I.

This paper discusses a bootstrap-based test, which checks if finite moments exist, and indicates cases of possible misapplication. It notes, that a procedure for finding the smallest power to which observations need to be raised, such that the test rejects a hypothesis that the corresponding moment is finite, works poorly as an estimator of the tail index or moment estimator. This is the case especially for very low- and high-order moments. Several examples of correct usage of the test are also shown. The main result is derived analytically, and a Monte-Carlo experiment is presented.