Advances and Applications in Statistics
Volume 38, Issue 2, Pages 81 - 111
(February 2014)
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A LEAST SQUARE METHOD ON CONFIDENCE REGIONS FOR HIGH QUANTILE OF HEAVY TAILED DISTRIBUTIONS
Val Andrei Fajardo and Mei Ling Huang
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Abstract: High quantile estimation is important in many real life applications related to the fields of insurance, finance and engineering. However, estimating high quantiles for heavy tailed distributions is a difficult task, requiring, first, a suitable estimator for the tail index. The Hill estimator of the tail index has been widely used in the literature. Based on the Hill estimator, a semi-parametric high quantile estimator is called the Hill-Weissman estimator. The asymptotic distribution of the Hill-Weissman estimator obtains approximate confidence regions for high quantiles. This paper proposes a new estimator for high quantiles of a heavy tailed distribution based on the least squares methodology. The asymptotic distribution of this estimator is also analyzed, hence providing for a new approximate confidence region for high quantiles. Computational simulations show that the new estimators are more efficient than the Hill-Weissman method. Finally, the performances of the estimation methods are compared when applied to two real world data sets. |
Keywords and phrases: bias, efficiency, generalized Pareto distribution, goodness of fit test, Hill estimator, least square, order statistics, probability coverage, tail index, Weissman estimator. |
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