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 Electronic Communications in Probability > Vol. 13 (2008) > Paper 48 open journal systems 


Limit theorems for multi-dimensional 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.


Full text: PDF

Pages: 507-517

Published on: October 13, 2008
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Electronic Communications in Probability. ISSN: 1083-589X