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Limit theorems for multi-dimensional random quantizers


 
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1. Title Title of document Limit theorems for multi-dimensional random quantizers
 
2. Creator Author's name, affiliation, country Joseph Yukich; Lehigh University
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Quantization; laws of large numbers; central limit theorems; stabilization
 
3. Subject Subject classification Primary 60F05; Secondary 60D05
 
4. Description Abstract We consider the $r$-th 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 $d \geq 1$ and $r \in (0, \infty)$ we establish mean and variance asymptotics as well as central limit theorems for the $r$-th 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 $X_i, 1 \leq i \leq n,$ a mass equal to the local distortion.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) National Security Agency
 
7. Date (YYYY-MM-DD) 2008-10-13
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1418
 
10. Identifier Digital Object Identifier 10.1214/ECP.v13-1418
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 13
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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