On the rate of convergence of the sum of the sample extremes |
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Authors: | Joop Mijnheer |
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Institution: | (1) Department of Mathematics, University of Leiden, 2300 RA Leiden, The Netherlands |
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Abstract: | Summary Let X
1, X
2,..., X
n
be independent random variables having a common distribution in the domain of normal attraction of a completely asymmetric stable law with characteristic exponent }(0,1) and support bounded below. Let X
n:n
X
n:n
-1 ... X
n:1
denote the ordered sample. We obtain the rate of convergence of n
-1/ (X
n:n
+...+X
n:n-k
n+1
) to the stable limit law as both n and k
n
» . As a consequence we obtain a representation of the sum X
n:n
+...+X
n:n-k
n+1
. |
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Keywords: | |
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