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Uniform decomposition of probability measures: quantization, clustering and rate of convergence
- Source :
- Journal of Applied Probability, Journal of Applied Probability, Cambridge University press, 2018, 55 (4), pp.1037-1045. ⟨10.1017/jpr.2018.69⟩, Journal of Applied Probability, 2018, 55 (4), pp.1037-1045. ⟨10.1017/jpr.2018.69⟩
- Publication Year :
- 2018
- Publisher :
- Cambridge University Press (CUP), 2018.
-
Abstract
- The study of finite approximations of probability measures has a long history. In Xu and Berger (2017), the authors focused on constrained finite approximations and, in particular, uniform ones in dimensiond=1. In the present paper we give an elementary construction of a uniform decomposition of probability measures in dimensiond≥1. We then use this decomposition to obtain upper bounds on the rate of convergence of the optimal uniform approximation error. These bounds appear to be the generalization of the ones obtained by Xu and Berger (2017) and to be sharp for generic probability measures.
- Subjects :
- Statistics and Probability
Approximations of π
Computer Science::Information Retrieval
General Mathematics
Quantization (signal processing)
010103 numerical & computational mathematics
Rate of convergence
Mathematical Subject Classification: 60E15, 62E17, 60B10, 60F99
01 natural sciences
Minimax approximation algorithm
Clustering
Uniform approximation
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
010104 statistics & probability
Quantization
Applied mathematics
Wasserstein distance
0101 mathematics
Statistics, Probability and Uncertainty
Cluster analysis
Probability measure
Mathematics
Subjects
Details
- ISSN :
- 14756072 and 00219002
- Volume :
- 55
- Database :
- OpenAIRE
- Journal :
- Journal of Applied Probability
- Accession number :
- edsair.doi.dedup.....ed8ca7c26004b35ff41232a855ce2c10