What does estimator of the tail index or moment estimator me

This paper discusses a bootstrap-based test that checks if finite moments exist and indicates cases of possible misapplication. It notes, in fact, that a procedure for finding the smallest power to which a sample needs 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. Several examples of correct usage of the test are also shown. The main result is derived analytically, and a numerical Monte-Carlo example Is presented.

Solution

The tail index is the one useful to measure the area under a tailed distribution. It is most used the significance level as a tail index in most cases.

The moment estimator is the mean of the nth power of a random variable. The moment is defined to be a tool to use the method of moments, which is useful to estimate population parameters, therefore, to characterize a probability distribution to fit best a population.