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May 2004

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Subject:
From:
Daniil Riabko <[log in to unmask]>
Reply To:
Classification, clustering, and phylogeny estimation
Date:
Mon, 10 May 2004 21:55:01 +0100
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Hi All ,

does anybody know an upper bound for the probability of the
 largest Voronoi cell?
 More precisely, let x_1 ... x_n be drawn randomly and independently
according
 to a distribution P on R^d. I'm looking for an upper bound of

  E ( max_{i=1..n} P(B_i) )

 where B_i is the Voronoi cell containing x_i, i.e.
 B_i={x: x_i is the nearest neighbour of x among x_1,...,x_n}

 I guess this should be O(1/n) ... but not sure.

thanks,
Daniil

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