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Original Articles

Large Deviation Principles for Sequences of Maxima and Minima

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Pages 1077-1098 | Received 05 Jan 2012, Accepted 17 Feb 2012, Published online: 14 Feb 2014

References

  • Arnold , B. C. , Balakrishnan , N. , Nagaraja , H. N. ( 1992 ). A First Course in Order Statistics . New York : John Wiley and Sons .
  • Beirlant , J. , Goegebeur , Y. , Teugels , J. , Segers , J. ( 2004 ). Statistics of Extremes. Theory and Applications . Chichester : John Wiley and Sons .
  • Bingham , N. H. , Goldie , C. M. , Teugels , J. ( 1987 ). Regular Variation . Cambridge : Cambridge University Press .
  • Coles , S. ( 2001 ). An Introduction to Statistical Modeling of Extreme Values . London : Springer-Verlag .
  • Cover , T. M. , Thomas , J. A. , ( 1991 ). Elements of Information Theory . New York : John Wiley and Sons .
  • Davis , R. A. ( 1979 ). Maxima and minima of stationary sequences. Ann. Probab. 453 – 460 .
  • de Haan , L. ( 1970 ). On Regular Variation and its Application to Weak Convergence of Sample Extremes . Amsterdam : CWI Tract, 32 .
  • de Haan , L. , Ferreira , A. ( 2006 ). Extreme Value Theory. An Introduction . New York : Springer .
  • Dembo , A. , Zeitouni , O. ( 1998 ). Large Deviations Techniques and Applications. Second Edition . New York : Springer .
  • Embrechts , P. , Klüppelberg , C. , Mikosch , T. ( 1997 ). Modelling Extremal Events . Berlin : Springer .
  • Falk , M. , Hüsler , J. , Reiss , R. D. ( 2004 ). Laws of Small Numbers: Extremes and Rare Events. Second Edition . Basel : Birkhäuser Verlag .
  • Finkenstädt , B. , Rootzén , H. ( 2004 ). Extreme Values in Finance, Telecommunications and the Environment . Berlin : Chapman and Hall/CRC .
  • Galambos , J. ( 1987 ). The Asymptotic Theory of Extreme Order Statistics. Second Edition . Malabar : Krieger .
  • Kotz , S. , Nadarajah , S. ( 2000 ). Extreme Value Distributions . London : Imperial College Press .
  • Leadbetter , M. R. , Lindgren , G. , Rootzén , H. ( 1983 ). Extremes and Related Properties of Random Sequences and Processes . Berlin : Springer-Verlag .
  • Lynch , J. , Sethuraman , J. ( 1987 ). Large deviations for processes with independent increments . Ann. Probab. 15 : 610 – 627 .
  • Macci , C. ( 2010 ). Large deviations for estimators of some threshold parameters . Stat. Methods Appl. 19 : 63 – 77 .
  • Mikosch , T. , Nagaev , A. V. ( 1998 ). Large deviations of heavy-tailed sums with applications in insurance . Extremes 1 : 81 – 110 .
  • Nagaev , A. V. ( 1969 ). Integral limit theorems taking large deviations into account when Cramér's condition does not hold I–II. Theory Probab. Appl. 14 : 51 – 64 and 193 – 208 .
  • Nagaev , S. V. ( 1979 ). Large deviations of sums of independent random variables . Ann. Probab. 7 : 745 – 789 .
  • Reiss , R. D. , Thomas , M. ( 2007 ). Statistical Analysis of Extreme Values with Applications to Insurance, Finance, Hydrology and Other Fields. Third edition . Basel : Birkhäuser Verlag .
  • Resnick , S. I. ( 1987 ). Extreme Values, Regular Variation, and Point Processes . New York : Springer .
  • Resnick , S. I. ( 1972 ). Stability of maxima of random variables defined on a Markov chain . Advances in Appl. Probability 4 : 285 – 295 .
  • Schmitz , V. ( 2004 ). Revealing the dependence structure between X(1) and X(n) . J. Statist. Plann. Inference 123 : 41 – 47 .

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