Limit theory for multivariate sample extremes

  • Laurens de Haan
  • Sidney I. Resnick


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.


Stochastic Process Probability Theory Random Vector Mathematical Biology Weak Convergence 
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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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