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Limit theory for multivariate sample extremes

  • Laurens de Haan
  • Sidney I. Resnick
Article

Summary

Let \(\{ (X_n^{(1)} ),...,X_n^{(k)} ,{\text{ }}n\} \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \geqslant } 1\} \) be k-dimensional iid random vectors. Necessary and sufficient conditions are found for the weak convergence of the maxima \(\left\{ {\mathop {\text{V}}\limits_{j{\text{ = 1}}}^n X_j^{(1)} ,...,\mathop {\text{V}}\limits_{j{\text{ = 1}}}^n X_j^{(k)} } \right\}\) suitably normed to a non-degenerate limit df.

The class of such limits is specified and conditions stated for the limit joint df to be a product of marginal df's. Some results are presented concerning extremal processes generated by multivariate df's.

Keywords

Stochastic Process Probability Theory Random Vector Mathematical Biology Weak Convergence 
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.

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Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • Laurens de Haan
    • 1
    • 2
  • Sidney I. Resnick
    • 1
    • 2
  1. 1.Econometric Institute Burgemeester Oudlaan 50Erasmus University RotterdamRotterdam
  2. 2.Department of StatisticsHolland and Colorado State UniversityFort CollinsUSA

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