Rates of convergence in the operator-stable limit theorem |
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Authors: | Makoto Maejima Svetlozar T Rachev |
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Institution: | (1) Department of Mathematics, Keio University, Hiyoshi, 223 Yokohama, Japan;(2) Department of Statistics and Applied Probability, University of California, 93106 Santa Barabara, California |
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Abstract: | Suppose that the
d
-valued random vector is strictly operator-stable in the sense that
, the characteristic function of , satisfies
for everyt<0, for some invertible linear operatorB on
d
. Suppose also that for the i.i.d. random vectors {X
i
} in
d
,
. In the present paper, we study the rates of convergence of this operator-stable limit theorem in terms of several probability metrics. A new type of ideal metrics suitable for this rate-of-convergence problem is introduced.This research was partially supported by NSF, Grant DMS-9103452 and NATO, Grant CRG900798. |
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Keywords: | Operator-stable distributions probability metrics rate of convergence |
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