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  • 1
    Electronic Resource
    Electronic Resource
    Local Asymptotic Normality in Extreme Value Index Estimation (1997)
    Springer
    Annals of the Institute of Statistical Mathematics 49 (1997), S. 645-666 
    Details
    ISSN: 1572-9052
    Keywords: Extreme value distribution ; extreme value index ; domain of attraction ; generalized Pareto distribution ; Hill estimator ; local asymptotic normality ; central sequence ; asymptotic efficiency
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper deals with the estimation of the extreme value index in local extreme value models. We establish local asymptotic normality (LAN) under certain extreme value alternatives. It turns out that the central sequence occurring in the LAN expansion of the likelihood process is up to a rescaling procedure the Hill estimator. The central sequence plays a crucial role for the construction of asymptotic optimal statistical procedures. In particular, the Hill estimator is asymptotically minimax.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1003210125157
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Testing the Gumbel Hypothesis Via the Pot-Method (1998)
    Springer
    Extremes 1 (1998), S. 191-213 
    Details
    ISSN: 1572-915X
    Keywords: extreme value distribution ; generalized Pareto distribution ; domain of attraction ; point process of exceedances ; peaks over threshold ; local asymptotic normality ; local extreme value alternative ; central sequence ; asymptotically optimal test ; adaptivity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider an i.i.d. sample, generated by some distribution function, which belongs to the domain of attraction of an extreme value distribution with unknown shape and scale parameters. We treat the scale parameter as a nuisance parameter and establish for the hypothesis of Gumbel domain of attraction an asymptotically optimal test based on those observations among the sample, which exceed a given threshold sequence. Asymptotic optimality is achieved along certain contiguous extreme value alternatives within the concept of local asymptotic normality (LAN). Adaptive test procedures exist under restrictive assumptions. The finite sample size behavior of the proposed test is studied by simulations and it is compared to that of a test based on the sample coefficient of variation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009910806693
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  • 3
    Electronic Resource
    Electronic Resource
    Testing Extreme Value Models (2000)
    Springer
    Extremes 3 (2000), S. 363-384 
    Details
    ISSN: 1572-915X
    Keywords: extreme value distribution ; generalized Pareto distribution ; local asymptotic normality ; asymptotically uniformly optimal test ; asymptotic envelope power function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider the full statistical families of extreme value distributions $$G_{\beta ,\sigma ,\mu } $$ and generalized Pareto distributions $$H_{\beta ,\sigma ,\mu } $$ , where $$\beta \in \mathbb{R},\sigma 〉 0$$ , and $$\mu \in \mathbb{R}$$ denote the shape, scale and location parameters, respectively. We consider the testing problems $$\beta \geqslant 0$$ against $$\beta 〈 0$$ and β = 0 against β ≠ 0, where σ and μ are treated as nuisance parameters. Showing local asymptotic normality (LAN), we derive asymptotic envelope power functions for test sequences and establish tests which attain these upper bounds. The finite sample size behavior is studied by simulations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1012209826248
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  • 4
    Electronic Resource
    Electronic Resource
    Global sufficiency of extreme order statistics in location models of Weibull type (1991)
    Springer
    Probability theory and related fields 88 (1991), S. 261-268 
    Details
    ISSN: 1432-2064
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In Janssen and Reiss (1988) it was shown that in a location model of a Weibull type sample with shape parameter −1〈a〈1 thek(n) lower extremes are asymptotically local sufficient. In the present paper we show that even global sufficiency holds. Moreover, it turns out that convergence of the given statistical experiments in the deficiency metric does not only hold for compact parameter sets but for the whole real line.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01212562
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  • 5
    Book
    Book
    Angewandte Statisik mit SAS : eine Einführung + Diskette (1995)
    Berlin u.a. :Springer,
    Details
    Title: Angewandte Statisik mit SAS : eine Einführung + Diskette
    Author: Falk, Michael
    Contributer: Becker, Rainer , Marohn, Frank
    Publisher: Berlin u.a. :Springer,
    Year of publication: 1995
    Pages: 393 S.
    Type of Medium: Book
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