L_p and almost sure convergence of estimation on heavy tail index under random censoring
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In this paper, we prove L_p, p≥ 2 and almost sure convergence of tail index estimator mentioned in grama2008 under random censoring and several assumptions. pth moment of the error of the estimator is proved to be of order O(1/^mκ/2n) 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.
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