Estimating Pareto Tail Index Based on Sample Means
نویسندگان
چکیده
• We propose an estimator of the Pareto tail index m of a distribution, that competes well with the Hill, Pickands and moment estimators. Unlike the above estimators, that are based only on the extreme observations, the proposed estimator uses all observations; its idea rests in the tail behavior of the sample mean X̄n, having a simple structure under heavy-tailed F . The observations, partitioned into N independent samples of sizes n, lead to N sample means whose empirical distribution function is the main estimation tool. The estimator is strongly consistent and asymptotically normal as N → ∞, while n remains fixed. Its behavior is illustrated in a simulation study. Key-Words: • domain of attraction; Pareto index; strong embedding of empirical process; tail behavior. AMS Subject Classification: • 62G05, 62G30. 76 A. Fialová, J. Jurečková and J. Picek Estimating Pareto Tail Index Based on Sample Means 77
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