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February 2006 Central limit theorem and convergence to stable laws in Mallows distance
Oliver Johnson, Richard Samworth
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Bernoulli 12(1): 191-191 (February 2006).


Bernoulli 11(5), 2005, 829-845. It has recently come to our attention that there is a large overlap between our Theorem 1.2 and the work of Tanaka (1973) and Cuesta and Matran (1989). In particular, the same result as ours is proved in both cases by analysing the same subadditive sequence, for real-valued random variables in Tanaka (1973) and in the more general Hilbert space setting in Cuesta and Matran (1989). Both these papers assume the stronger condition of a finite fourth moment, though they both comment that this can be weakened, perhaps to just requiring a finite (2 + δ)th moment, for δ > 0. In our paper we need only a finite second moment. We acknowledge the priority of the above authors on this result and sincerely apologize for our oversight.


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Oliver Johnson. Richard Samworth. "Central limit theorem and convergence to stable laws in Mallows distance." Bernoulli 12 (1) 191 - 191, February 2006.


Published: February 2006
First available in Project Euclid: 28 February 2006

zbMATH: 1126.60018
MathSciNet: MR2202329

Rights: Copyright © 2006 Bernoulli Society for Mathematical Statistics and Probability


Vol.12 • No. 1 • February 2006
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