A new method for estimating the tail index using truncated sample sequence

F. Q. Tang; D. Han

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arXiv · 2209.04772

A new method for estimating the tail index using truncated sample sequence

F. Q. Tang·D. Han

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Abstract

This article proposes a new method of truncated estimation to estimate the tail index $\alpha$ of the extremely heavy-tailed distribution with infinite mean or variance. We not only present two truncated estimators $\hat{\alpha}$ and $\hat{\alpha}^{\prime}$ for estimating $\alpha$ ($0<\alpha \leq 1$) and $\alpha$ ($1<\alpha \leq 2$) respectively, but also prove their asymptotic statistical properties. The numerical simulation results comparing the six known estimators in estimating error, the Type I Error and the power of estimator show that the performance of the two new truncated estimators is quite good on the whole.

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F. Q. Tang, D. Han. 2022-09-11. A new method for estimating the tail index using truncated sample sequence. https://arxiv.org/abs/2209.04772

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