Measure Concentration for Compound Poisson Distributions
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2005
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| _version_ | 1866909191498629120 |
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| author | Kontoyiannis, I. Madiman, M. |
| author_facet | Kontoyiannis, I. Madiman, M. |
| contents | We give a simple development of the concentration properties of compound Poisson measures on the nonnegative integers. A new modification of the Herbst argument is applied to an appropriate modified logarithmic-Sobolev inequality to derive new concentration bounds. When the measure of interest does not have finite exponential moments, these bounds exhibit optimal polynomial decay. Simple new proofs are also given for earlier results of Houdr{é} (2002) and Wu (2000). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0506435 |
| institution | arXiv |
| publishDate | 2005 |
| record_format | arxiv |
| spellingShingle | Measure Concentration for Compound Poisson Distributions Kontoyiannis, I. Madiman, M. Probability 60E07, 60E15, 46N30, 39B62 We give a simple development of the concentration properties of compound Poisson measures on the nonnegative integers. A new modification of the Herbst argument is applied to an appropriate modified logarithmic-Sobolev inequality to derive new concentration bounds. When the measure of interest does not have finite exponential moments, these bounds exhibit optimal polynomial decay. Simple new proofs are also given for earlier results of Houdr{é} (2002) and Wu (2000). |
| title | Measure Concentration for Compound Poisson Distributions |
| topic | Probability 60E07, 60E15, 46N30, 39B62 |
| url | https://arxiv.org/abs/math/0506435 |