Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Basu, D. (1955). On statistics independent of a complete sufficient statistic, Sankhya, 15, 377–380.
Berman, S. (1962a). A law of large numbers for the maximum in a stationary Gaussian sequence, Ann. Math. Stat., 33, 93–97.
Berman, S. (1962b). Limiting distribution of the maximum term in sequences of dependent random variables, Ann. Math. Stat., 33, 894–908.
Berman, S. (1964). Limit theorem for the maximum term in stationary sequences, Ann. Math. Stat., 35, 502–516.
Cramér, H. (1962). On the maximum of a normal stationary stochastic process, Bull. Am. Math. Soc., 68, 512–516.
Galambos, J.(1977). The Asymptotic Theory of Extreme Order Statistics, Academic Press, New York.
Gnedenko, B. (1943). Sur la distribution limite du terme maximum d’une serie aleatoire, Ann. Math., 2(44), 423–453.
Hall, P. (1979). On the rate of convergence of normal extremes, J. Appl. Prob., 16(2), 433–439.
Leadbetter, M. (1974). On extreme values in stationary sequences, Z. Wahr. Verw. Geb., 28, 289–303.
Leadbetter, M., Lindgren, G., and Rootzén, H. (1983). Extremes and Related Properties of Random Sequences and Processes, Springer, New York.
Loynes, R. (1965). Extreme values in uniformly mixing stationary stochastic processes, Ann. Math. Stat., 36, 993–999.
McCormick, W. (1980). Weak convergence for the maximum of stationary Gaussian processes using random normalization, Ann. Prob., 8, 483–497.
Mittal, Y. (1974). Limiting behavior of maxima in stationary Gaussian sequences, Ann. Prob., 2, 231–242.
Mittal, Y. and Ylvisaker, D. (1975). Limit distribution for the maxima of stationary Gaussian processes, Stoch. Proc. Appl., 3, 1–18.
Pickands, J. (1967). Maxima of stationary Gaussian processes, Z. Wahr. Verw. Geb., 7, 190–223.
Reiss, R. (1989). Approximate Distributions of Order Statistics, with Applications to Nonparametric Statistics, Springer-Verlag, New York.
Sen, P.K. and Singer, J. (1993). Large Sample Methods in Statistics: An Introduction with Applications, Chapman and Hall, New York.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-0-387-75971-5_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-75970-8
Online ISBN: 978-0-387-75971-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)