Stein approximation for functionals of independent random sequences
We derive Stein approximation bounds for functionals of uniform random variables, using chaos expansions and the Clark-Ocone representation formula combined with derivation and finite difference operators. This approach covers sums and functionals of both continuous and discrete independent random v...
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| Format: | Journal Article |
| Language: | English |
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2018
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| Online Access: | https://hdl.handle.net/10356/88783 http://hdl.handle.net/10220/44722 |
| _version_ | 1811690708516470784 |
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| author | Privault, Nicolas Serafin, Grzegorz |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Privault, Nicolas Serafin, Grzegorz |
| author_sort | Privault, Nicolas |
| collection | NTU |
| description | We derive Stein approximation bounds for functionals of uniform random variables, using chaos expansions and the Clark-Ocone representation formula combined with derivation and finite difference operators. This approach covers sums and functionals of both continuous and discrete independent random variables. For random variables admitting a continuous density, it recovers classical distance bounds based on absolute third moments, with better and explicit constants. We also apply this method to multiple stochastic integrals that can be used to represent U-statistics, and include linear and quadratic functionals as particular cases. |
| first_indexed | 2024-10-01T06:08:17Z |
| format | Journal Article |
| id | ntu-10356/88783 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T06:08:17Z |
| publishDate | 2018 |
| record_format | dspace |
| spelling | ntu-10356/887832023-02-28T19:35:56Z Stein approximation for functionals of independent random sequences Privault, Nicolas Serafin, Grzegorz School of Physical and Mathematical Sciences Independent Sequences Uniform Distribution We derive Stein approximation bounds for functionals of uniform random variables, using chaos expansions and the Clark-Ocone representation formula combined with derivation and finite difference operators. This approach covers sums and functionals of both continuous and discrete independent random variables. For random variables admitting a continuous density, it recovers classical distance bounds based on absolute third moments, with better and explicit constants. We also apply this method to multiple stochastic integrals that can be used to represent U-statistics, and include linear and quadratic functionals as particular cases. MOE (Min. of Education, S’pore) Published version 2018-04-26T04:22:53Z 2019-12-06T17:10:50Z 2018-04-26T04:22:53Z 2019-12-06T17:10:50Z 2018 Journal Article Privault, N., & Serafin, G. (2018). Stein approximation for functionals of independent random sequences. Electronic Journal of Probability, 23(2018), 4-. https://hdl.handle.net/10356/88783 http://hdl.handle.net/10220/44722 10.1214/17-EJP132 en Electronic Journal of Probability © 2018 The Author(s) (published by Bernouli Society and the Institute of Mathematical Statistics). This paper was published in Electronic Journal of Probability and is made available as an electronic reprint (preprint) with permission of Bernouli Society and the Institute of Mathematical Statistics. The published version is available at: [http://dx.doi.org/10.1214/17-EJP132]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law. 34 p. application/pdf |
| spellingShingle | Independent Sequences Uniform Distribution Privault, Nicolas Serafin, Grzegorz Stein approximation for functionals of independent random sequences |
| title | Stein approximation for functionals of independent random sequences |
| title_full | Stein approximation for functionals of independent random sequences |
| title_fullStr | Stein approximation for functionals of independent random sequences |
| title_full_unstemmed | Stein approximation for functionals of independent random sequences |
| title_short | Stein approximation for functionals of independent random sequences |
| title_sort | stein approximation for functionals of independent random sequences |
| topic | Independent Sequences Uniform Distribution |
| url | https://hdl.handle.net/10356/88783 http://hdl.handle.net/10220/44722 |
| work_keys_str_mv | AT privaultnicolas steinapproximationforfunctionalsofindependentrandomsequences AT serafingrzegorz steinapproximationforfunctionalsofindependentrandomsequences |