
Limit theorems for multidimensional random quantizers

Joseph Yukich, Lehigh University 
Abstract
We consider the $rth$ power quantization error arising
in the optimal approximation of a $d$dimensional probability
measure $P$ by a discrete measure supported by the realization of
$n$ i.i.d. random variables $X_1,...,X_n$. For all $d ≥ 1$ and
$r in (0, ∞)$ we establish mean and variance asymptotics as
well as central limit theorems for the $rth$ power quantization
error. Limiting means and variances are expressed in terms of the
densities of $P$ and $X_1$. Similar convergence results hold for
the random point measures arising by placing at each $X_i, 1
≤ i ≤ n,$ a mass equal to the local distortion.

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Pages: 507517
Published on: October 13, 2008

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