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References

  • Basu, D. (1955). On statistics independent of a complete sufficient statistic, Sankhya, 15, 377–380.

    MATH  MathSciNet  Google Scholar 

  • Berman, S. (1962a). A law of large numbers for the maximum in a stationary Gaussian sequence, Ann. Math. Stat., 33, 93–97.

    Article  MATH  Google Scholar 

  • Berman, S. (1962b). Limiting distribution of the maximum term in sequences of dependent random variables, Ann. Math. Stat., 33, 894–908.

    Article  MATH  Google Scholar 

  • Berman, S. (1964). Limit theorem for the maximum term in stationary sequences, Ann. Math. Stat., 35, 502–516.

    Article  MATH  Google Scholar 

  • Cramér, H. (1962). On the maximum of a normal stationary stochastic process, Bull. Am. Math. Soc., 68, 512–516.

    MATH  Google Scholar 

  • Galambos, J.(1977). The Asymptotic Theory of Extreme Order Statistics, Academic Press, New York.

    Google Scholar 

  • Gnedenko, B. (1943). Sur la distribution limite du terme maximum d’une serie aleatoire, Ann. Math., 2(44), 423–453.

    Article  MathSciNet  Google Scholar 

  • Hall, P. (1979). On the rate of convergence of normal extremes, J. Appl. Prob., 16(2), 433–439.

    Article  MATH  Google Scholar 

  • Leadbetter, M. (1974). On extreme values in stationary sequences, Z. Wahr. Verw. Geb., 28, 289–303.

    Article  MATH  MathSciNet  Google Scholar 

  • Leadbetter, M., Lindgren, G., and Rootzén, H. (1983). Extremes and Related Properties of Random Sequences and Processes, Springer, New York.

    MATH  Google Scholar 

  • Loynes, R. (1965). Extreme values in uniformly mixing stationary stochastic processes, Ann. Math. Stat., 36, 993–999.

    Article  MathSciNet  MATH  Google Scholar 

  • McCormick, W. (1980). Weak convergence for the maximum of stationary Gaussian processes using random normalization, Ann. Prob., 8, 483–497.

    Article  MATH  MathSciNet  Google Scholar 

  • Mittal, Y. (1974). Limiting behavior of maxima in stationary Gaussian sequences, Ann. Prob., 2, 231–242.

    Article  MATH  MathSciNet  Google Scholar 

  • Mittal, Y. and Ylvisaker, D. (1975). Limit distribution for the maxima of stationary Gaussian processes, Stoch. Proc. Appl., 3, 1–18.

    Article  MATH  MathSciNet  Google Scholar 

  • Pickands, J. (1967). Maxima of stationary Gaussian processes, Z. Wahr. Verw. Geb., 7, 190–223.

    Article  MATH  MathSciNet  Google Scholar 

  • Reiss, R. (1989). Approximate Distributions of Order Statistics, with Applications to Nonparametric Statistics, Springer-Verlag, New York.

    MATH  Google Scholar 

  • Sen, P.K. and Singer, J. (1993). Large Sample Methods in Statistics: An Introduction with Applications, Chapman and Hall, New York.

    Google Scholar 

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DasGupta, A. (2008). Sample Extremes. In: Asymptotic Theory of Statistics and Probability. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-75971-5_8

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