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March, 1985 Adaptive Estimates of Parameters of Regular Variation
Peter Hall, A. H. Welsh
Ann. Statist. 13(1): 331-341 (March, 1985). DOI: 10.1214/aos/1176346596


The problem of estimating shape and scale parameters for a distribution with regularly varying tails is related to that of nonparametrically estimating a density at a fixed point, in that optimal construction of the estimators depends substantially upon unknown features of the distribution. We show how to overcome this problem by using adaptive methods. Our main results hold very generally, for a large class of adaptive estimators. Later we consider specific versions of adaptive estimators, and describe their performance both in theory and by means of simulation studies. We also examine a technique proposed by Hill (1975) for solving similar problems.


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Peter Hall. A. H. Welsh. "Adaptive Estimates of Parameters of Regular Variation." Ann. Statist. 13 (1) 331 - 341, March, 1985.


Published: March, 1985
First available in Project Euclid: 12 April 2007

zbMATH: 0605.62033
MathSciNet: MR773171
Digital Object Identifier: 10.1214/aos/1176346596

Primary: 60G05
Secondary: 60E05, 60F17, 62F35

Rights: Copyright © 1985 Institute of Mathematical Statistics


Vol.13 • No. 1 • March, 1985
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