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CONVERGENCE RATES FOR THE MOMENTS OF EXTREMES

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초록

Let X1, X2,${\ldots}$, $X_n$ be a sequence of independent and identically distributed random variables with common distribution function $F$. Convergence rates for the moments of extremes are studied by virtue of second order regularly conditions. A unified treatment is also considered under second order von Mises conditions. Some examples are given to illustrate the results.

Abstract

Let X1, X2,${\ldots}$, $X_n$ be a sequence of independent and identically distributed random variables with common distribution function $F$. Convergence rates for the moments of extremes are studied by virtue of second order regularly conditions. A unified treatment is also considered under second order von Mises conditions. Some examples are given to illustrate the results.

참고문헌 (14)

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  2. L. de Haan, "Extreme Value Theory: An Introduction" (2006), Springer-Verlag
  3. L. de Haan, "Second order regular variation and rates of convergence in extreme value theory", Ann. Probab, 24(1), pp.97~124 (1996)
  4. L. de Haan, "Generalized regular variation of second order", J. Austral. Math. Soc. Ser. A, 61(3), pp.381~395 (1996)
  5. J. L. Geluk, "On the domain of attraction of exp(exp(-x))", Statist. Probab. Lett, 31(2), pp.91~95 (1996)
  6. J. L. Geluk, "Regular variation, Extensions and Tauberian Theorems", CWI Tract, 40. Stichting Mathematisch Centrum, Centrum voor Wiskunde en Informatica, ~ (1987)
  7. M. I. Gomes, "Approximation by penultimate extreme value distributions", Extremes, 2(1), pp.71~85 (1999)
  8. P. Hall, "On the rate of convergence of normal extremes", J. Appl. Probab, 16(2), pp.433~439 (1979)
  9. W. J. Hall, "The rate of convergence in law of the maximum of an exponential sample", Statist. Neerlandica, 33(3), pp.151~154 (1979)
  10. E. Kaufmann, "Penultimate approximations in extreme value theory", Extremes, 3(1), pp.39~55 (2000)
  11. K. Liu, "The convergence rates of conditional moments", Journal of Southwest University (Natural Science), 29, pp.5~8 (2007)
  12. Z. Peng, "Conditions based on conditional moment for max- stable limit laws", Extremes, 11(4), pp.329~337 (2008)
  13. J. Pickands, "Moment convergence of sample extremes", Ann. Math. Statist, 39, pp.881~889 (1968)
  14. S. I. Resnick, "Extreme Values, Regular Variation and Point Processes" (1987), Springer-Verlag

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