Testing for the shape parameter of generalized extreme value distribution based on the $$L_q$$ -likelihood ratio statistic

Chao Huang, Jin-Guan Lin () and Yan-Yan Ren

Metrika: International Journal for Theoretical and Applied Statistics, 2013, vol. 76, issue 5, 671 pages

Abstract: This paper studies the applications of extreme value theory on analysis for closing price data of the Dow-Jones industrial index and Danish fire insurance claims data. The generalized extreme value (GEV) distribution is considered in analyzing the real data, and the hypothesis testing problem for the shape parameter of GEV distribution is investigated based on a new test statistic—the $$L_q$$ -likelihood ratio ( $$L_q$$ R) statistic. The $$L_q$$ R statistic can be treated as a generalized form of the classical likelihood ratio (LR) statistic. We show that the asymptotic behavior of proposed statistic is characterized by the degree of distortion $$q$$ . For small and modest sample sizes, the $$L_q$$ R statistic is still available when $$q$$ is properly chosen. By simulation studies, the proposed statistic not only performs the asymptotic properties, but also outperforms the classical LR statistic as the sample sizes are modest or even small. Meanwhile, the test power based on the new statistic is also simulated by Monte Carlo methods. At last, the models are diagnosed by graphical methods. Copyright Springer-Verlag 2013

Keywords: Hypothesis testing; $$L_q$$ -likelihood ratio statistic; Generalized extreme value distribution; Bootstrap method; Maximum $$L_q$$ -likelihood estimate (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:spr:metrik:v:76:y:2013:i:5:p:641-671

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DOI: 10.1007/s00184-012-0409-5

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