Asymptotic normality of Hill Estimator for truncated data

2010/09/22 by Arijit Chakrabarty, Chakrabarty, Arijit
Economics, Econometrics and Finance · Mathematics · #62G32 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Statistics Theory (math.ST) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #math.ST #msc:62G32 #stat.TH

paper · pdf · doi:10.48550/arxiv.1009.4286

arxiv created 2010/09/22 · openalex publication_date 2010/09/22 · arxiv updated 2010/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The problem of estimating the tail index from truncated data is addressed in Chakrabarty and Samorodnitsky (2009). In that paper, a sample based (and hence random) choice of k is suggested, and it is shown that the choice leads to a consistent estimator of the inverse of the tail index. In this paper, the second order behavior of the Hill estimator with that choice of k is studied, under some additional assumptions. In the untruncated situation, it is well known that asymptotic normality of the Hill estimator follows from the assumption of second order regular variation of the underlying distribution. Motivated by this, we show the same in the truncated case in light of the second order regular variation.

Related

• Estimating the second-order parameter of regular variation and bias\n reduction in tail index estimation under random truncation
• Flexible Extreme Value Inference And Hill Plots For A Small, Mid And\n Large Samples
• Several new tail index estimators
• Semiparametric tail-index estimation for randomly right-truncated heavy-tailed data
• Trimming the Hill estimator: robustness, optimality and adaptivity