Weighted Moment Estimators for the Second Order Scale Parameter

Tertius de Wet (), Yuri Goegebeur () and Armelle Guillou ()
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Tertius de Wet: University of Stellenbosch
Yuri Goegebeur: University of Southern Denmark
Armelle Guillou: Université de Strasbourg et CNRS

Methodology and Computing in Applied Probability, 2012, vol. 14, issue 3, 753-783

Abstract: Abstract We consider the estimation of the scale parameter appearing in the second order condition when the distribution underlying the data is of Pareto-type. Inspired by the work of Goegebeur et al. (J Stat Plan Inference 140:2632–2652, 2010) on the estimation of the second order rate parameter, we introduce a flexible class of estimators for the second order scale parameter, which has weighted sums of scaled log spacings of successive order statistics as basic building blocks. Under the second order condition, some conditions on the weight functions, and for appropriately chosen sequences of intermediate order statistics, we establish the consistency of our class of estimators. Asymptotic normality is achieved under a further condition on the tail function 1 − F, the so-called third order condition. As the proposed estimator depends on the second order rate parameter, we also examine the effect of replacing the latter by a consistent estimator. The asymptotic performance of some specific examples of our proposed class of estimators is illustrated numerically, and their finite sample behavior is examined by a small simulation experiment.

Keywords: Extreme value statistics; Pareto-type model; Second order scale parameter; Weighted estimator; 62G05; 62G20; 62G30; 62G32 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s11009-011-9263-6

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