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A general estimator for the right endpoint with an application to supercentenarian women’s records. (English) Zbl 1367.62160

Summary: We extend the setting of the right endpoint estimator introduced in [the first two authors, Stat. Sin. 24, No. 4, 1811–1835 (2014; Zbl 1480.62084)] to the broader class of light-tailed distributions with finite endpoint, belonging to some domain of attraction induced by the extreme value theorem. This stretch enables a general estimator for the finite endpoint, which does not require estimation of the (supposedly non-positive) extreme value index. A new testing procedure for selecting max-domains of attraction also arises in connection with the asymptotic properties of the general endpoint estimator. The simulation study conveys that the general endpoint estimator is a valuable complement to the most usual endpoint estimators, particularly when the true extreme value index stays above \(-1/2\), embracing the most common cases in practical applications. An illustration is provided via an extreme value analysis of supercentenarian women data.

MSC:

62G32 Statistics of extreme values; tail inference
62F10 Point estimation
62P10 Applications of statistics to biology and medical sciences; meta analysis

Citations:

Zbl 1480.62084
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References:

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