$L_p$ and almost sure convergence of estimation on heavy tail index under random censoring

Yunyi Zhang; Jiazheng Liu; Zexin Pan; Dimitris N. Politis

$L_p$ and almost sure convergence of estimation on heavy tail index under random censoring

Statistics Theory 2018-08-28 v1 Statistics Theory

Authors: Yunyi Zhang , Jiazheng Liu , Zexin Pan , Dimitris N. Politis

Abstract

In this paper, we prove $L_p,\ p\geq 2$ and almost sure convergence of tail index estimator mentioned in \cite{grama2008} under random censoring and several assumptions. $p$ th moment of the error of the estimator is proved to be of order $O\left(\frac{1}{\log^{m\kappa/2}n}\right)$ with given assumptions. We also perform several finite sample simulations to quantify performance of this estimator. Finite sample results show that the proposed estimator is effective in finding underlying tail index even when censor rate is high.

Keywords

heavy tail index random censoring tail index estimator Lp convergence almost sure convergence finite sample simulation

Cite

@article{arxiv.1808.08320,
  title  = {$L_p$ and almost sure convergence of estimation on heavy tail index under random censoring},
  author = {Yunyi Zhang and Jiazheng Liu and Zexin Pan and Dimitris N. Politis},
  journal= {arXiv preprint arXiv:1808.08320},
  year   = {2018}
}

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There are totally 6 figures and 17 pages of this article

$L_p$ and almost sure convergence of estimation on heavy tail index under random censoring

Abstract

Keywords

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