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As a leading statistician in extreme value theory, Professor Laurens de Haan has made significant contribution in both probability
and statistics of extremes. In honor of his 70th birthday, we review testing issues in extremes, which include research done
by Professor Laurens de Haan and many others. In comparison with statistical estimation in extremes, research on testing has
received less attention. So we also point out some practical questions in this direction.
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Michael Falk 《Extremes》2008,11(1):55-80
Since the publication of his masterpiece on regular variation and its application to the weak convergence of (univariate)
sample extremes in 1970, Laurens de Haan (Thesis, Mathematical Centre Tract vol. 32, University of Amsterdam, 1970) is among the leading mathematicians in the world, with a particular focus on extreme value theory (EVT). On the occasion
of his 70th birthday it is a great pleasure and a privilege to follow his route through multivariate EVT, which started only seven years later in 1977, when Laurens de Haan published his first paper on multivariate EVT, jointly
with Sid Resnick.
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In the last decades there has been a shift from the parametric statistics of extremes for IID random variables, based on the
probabilistic asymptotic results in extreme value theory, towards a semi-parametric approach, where the estimation of the
right tail-weight, under a quite general framework, is of major importance. After a brief presentation of classical Gumbel’s
block methodology and of later improvements in the parametric framework (multivariate and multi-dimensional extreme value
models for largest observations and peaks over threshold approaches), we present a coordinated overview, over the last three
decades, of the developments on the estimation of the extreme value index under a semiparametric framework. Laurens de Haan
has been one of the leading scientists in the field, (co-)author of many seminal ideas, that he generously shared with dozens
(literally) of colleagues and students, thus achieving one of the main goals in a scientist’s life: he gathered around him
a bunch of colleagues united in the endeavour of building knowledge. The last section is a personal tribute to Laurens, who
fully lives his ideal that co-operation is the heart of Science.
To Laurens de Haan, a token of friendship. 相似文献
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Víctor Leiva 《商业与工业应用随机模型》2019,35(1):133-137
Sam C. Saunders, the son of Elizabeth Cundiff and Winston E. Saunders, was born in Richland, OR, on February 24, 1931. The family moved to La Grande, OR, in 1944, where Sam completed high school and two years at Eastern Oregon College. He then received the BSc degree in Mathematics from the University of Oregon, Eugene, OR, in 1952, and he attended the University of Washington, Seattle, WA, receiving a PhD degree under Z. W. Birnbaum. After graduating, he accepted employment at the Boeing Company in its Mathematical Services Unit and, in 1972, a position as a Full Professor at Washington State University, Pullman, WA, from which he retired in 1996. 相似文献
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Given a Hilbert spaceK generated by two of its subspaces,K=K
1K
2, we investigate the representation ofK inK
1K
2 which assigns to eachk K the pairPk=P(K
1)k P(K
2)k consisting of its orthogonal projections ontoK
1 andK
2.A part of this work was done during the visit of the second author at the University of Sevilla, Spain in September-October 1989. The support of Junta Andalusia is gratefully aknowledged. 相似文献
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Norbert J. Schmitz 《Mathematical Methods of Operations Research》1994,40(2):229-238
For a game-theoretical problem of optimal choice with interview costs and discounting we prove, using a saddle-point argument, the strict determinedness of the game and we give minimax strategies for both players. 相似文献
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