Chernoff bound (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Chernoff bound" in English language version.

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10doi.org

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7worldcat.org

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5arxiv.org

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5semanticscholar.org

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3web.archive.org

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3jstor.org

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2books.google.com

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2berkeley.edu

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1nowpublishers.com

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1crcpress.com

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1niss.org

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1sciencedirect.com

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1ncsu.edu

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1psu.edu

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1desmos.com

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arxiv.org

Tropp, Joel A. (2015-05-26). "An Introduction to Matrix Concentration Inequalities". Foundations and Trends in Machine Learning. 8 (1–2): 60. arXiv:1501.01571. doi:10.1561/2200000048. ISSN 1935-8237. S2CID 5679583.
Theodosopoulos, Ted (2007-03-01). "A reversion of the Chernoff bound". Statistics & Probability Letters. 77 (5): 558–565. arXiv:math/0501360. doi:10.1016/j.spl.2006.09.003. ISSN 0167-7152. S2CID 16139953.
Ahlswede, R.; Winter, A. (2003). "Strong Converse for Identification via Quantum Channels". IEEE Transactions on Information Theory. 48 (3): 569–579. arXiv:quant-ph/0012127. doi:10.1109/18.985947. S2CID 523176.
Tropp, J. (2010). "User-friendly tail bounds for sums of random matrices". Foundations of Computational Mathematics. 12 (4): 389–434. arXiv:1004.4389. doi:10.1007/s10208-011-9099-z. S2CID 17735965.
Magen, A.; Zouzias, A. (2011). "Low Rank Matrix-Valued Chernoff Bounds and Approximate Matrix Multiplication". arXiv:1005.2724 [cs.DM].

berkeley.edu

stat.berkeley.edu

Wainwright, M. (January 22, 2015). "Basic tail and concentration bounds" (PDF). Archived (PDF) from the original on 2016-05-08.

cs.berkeley.edu

Sinclair, Alistair (Fall 2011). "Class notes for the course "Randomness and Computation"" (PDF). Archived from the original (PDF) on 31 October 2014. Retrieved 30 October 2014.

books.google.com

Mitzenmacher, Michael; Upfal, Eli (2005). Probability and Computing: Randomized Algorithms and Probabilistic Analysis. Cambridge University Press. ISBN 978-0-521-83540-4.
Refer to this book section for more info on the problem.

crcpress.com

Chernoff, Herman (2014). "A career in statistics" (PDF). In Lin, Xihong; Genest, Christian; Banks, David L.; Molenberghs, Geert; Scott, David W.; Wang, Jane-Ling (eds.). Past, Present, and Future of Statistics. CRC Press. p. 35. ISBN 9781482204964. Archived from the original (PDF) on 2015-02-11.

desmos.com

See graphs of: the bound as a function of r when k changes and the bound as a function of k when r changes.

doi.org

Tropp, Joel A. (2015-05-26). "An Introduction to Matrix Concentration Inequalities". Foundations and Trends in Machine Learning. 8 (1–2): 60. arXiv:1501.01571. doi:10.1561/2200000048. ISSN 1935-8237. S2CID 5679583.
Chernoff, Herman (1952). "A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations". The Annals of Mathematical Statistics. 23 (4): 493–507. doi:10.1214/aoms/1177729330. ISSN 0003-4851. JSTOR 2236576.
Philips, Thomas K.; Nelson, Randolph (1995). "The Moment Bound Is Tighter Than Chernoff's Bound for Positive Tail Probabilities". The American Statistician. 49 (2): 175–178. doi:10.2307/2684633. ISSN 0003-1305. JSTOR 2684633.
Ghosh, Malay (2021-03-04). "Exponential Tail Bounds for Chisquared Random Variables". Journal of Statistical Theory and Practice. 15 (2): 35. doi:10.1007/s42519-020-00156-x. ISSN 1559-8616. S2CID 233546315.
Theodosopoulos, Ted (2007-03-01). "A reversion of the Chernoff bound". Statistics & Probability Letters. 77 (5): 558–565. arXiv:math/0501360. doi:10.1016/j.spl.2006.09.003. ISSN 0167-7152. S2CID 16139953.
Dillencourt, Michael; Goodrich, Michael; Mitzenmacher, Michael (2024). "Leveraging Parameterized Chernoff Bounds for Simplified Algorithm Analyses". Information Processing Letters. 187 (106516). doi:10.1016/j.ipl.2024.106516.
Hoeffding, W. (1963). "Probability Inequalities for Sums of Bounded Random Variables" (PDF). Journal of the American Statistical Association. 58 (301): 13–30. doi:10.2307/2282952. JSTOR 2282952.
Ahlswede, R.; Winter, A. (2003). "Strong Converse for Identification via Quantum Channels". IEEE Transactions on Information Theory. 48 (3): 569–579. arXiv:quant-ph/0012127. doi:10.1109/18.985947. S2CID 523176.
Tropp, J. (2010). "User-friendly tail bounds for sums of random matrices". Foundations of Computational Mathematics. 12 (4): 389–434. arXiv:1004.4389. doi:10.1007/s10208-011-9099-z. S2CID 17735965.
Goldberg, A. V.; Hartline, J. D. (2001). "Competitive Auctions for Multiple Digital Goods". Algorithms — ESA 2001. Lecture Notes in Computer Science. Vol. 2161. p. 416. CiteSeerX 10.1.1.8.5115. doi:10.1007/3-540-44676-1_35. ISBN 978-3-540-42493-2.; lemma 6.1

jstor.org

Chernoff, Herman (1952). "A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations". The Annals of Mathematical Statistics. 23 (4): 493–507. doi:10.1214/aoms/1177729330. ISSN 0003-4851. JSTOR 2236576.
Philips, Thomas K.; Nelson, Randolph (1995). "The Moment Bound Is Tighter Than Chernoff's Bound for Positive Tail Probabilities". The American Statistician. 49 (2): 175–178. doi:10.2307/2684633. ISSN 0003-1305. JSTOR 2684633.
Hoeffding, W. (1963). "Probability Inequalities for Sums of Bounded Random Variables" (PDF). Journal of the American Statistical Association. 58 (301): 13–30. doi:10.2307/2282952. JSTOR 2282952.

ncsu.edu

repository.lib.ncsu.edu

Hoeffding, W. (1963). "Probability Inequalities for Sums of Bounded Random Variables" (PDF). Journal of the American Statistical Association. 58 (301): 13–30. doi:10.2307/2282952. JSTOR 2282952.

niss.org

nisla05.niss.org

Chernoff, Herman (2014). "A career in statistics" (PDF). In Lin, Xihong; Genest, Christian; Banks, David L.; Molenberghs, Geert; Scott, David W.; Wang, Jane-Ling (eds.). Past, Present, and Future of Statistics. CRC Press. p. 35. ISBN 9781482204964. Archived from the original (PDF) on 2015-02-11.

nowpublishers.com

Tropp, Joel A. (2015-05-26). "An Introduction to Matrix Concentration Inequalities". Foundations and Trends in Machine Learning. 8 (1–2): 60. arXiv:1501.01571. doi:10.1561/2200000048. ISSN 1935-8237. S2CID 5679583.

psu.edu

citeseerx.ist.psu.edu

Goldberg, A. V.; Hartline, J. D. (2001). "Competitive Auctions for Multiple Digital Goods". Algorithms — ESA 2001. Lecture Notes in Computer Science. Vol. 2161. p. 416. CiteSeerX 10.1.1.8.5115. doi:10.1007/3-540-44676-1_35. ISBN 978-3-540-42493-2.; lemma 6.1

sciencedirect.com

Theodosopoulos, Ted (2007-03-01). "A reversion of the Chernoff bound". Statistics & Probability Letters. 77 (5): 558–565. arXiv:math/0501360. doi:10.1016/j.spl.2006.09.003. ISSN 0167-7152. S2CID 16139953.

semanticscholar.org

api.semanticscholar.org

Tropp, Joel A. (2015-05-26). "An Introduction to Matrix Concentration Inequalities". Foundations and Trends in Machine Learning. 8 (1–2): 60. arXiv:1501.01571. doi:10.1561/2200000048. ISSN 1935-8237. S2CID 5679583.
Ghosh, Malay (2021-03-04). "Exponential Tail Bounds for Chisquared Random Variables". Journal of Statistical Theory and Practice. 15 (2): 35. doi:10.1007/s42519-020-00156-x. ISSN 1559-8616. S2CID 233546315.
Theodosopoulos, Ted (2007-03-01). "A reversion of the Chernoff bound". Statistics & Probability Letters. 77 (5): 558–565. arXiv:math/0501360. doi:10.1016/j.spl.2006.09.003. ISSN 0167-7152. S2CID 16139953.
Ahlswede, R.; Winter, A. (2003). "Strong Converse for Identification via Quantum Channels". IEEE Transactions on Information Theory. 48 (3): 569–579. arXiv:quant-ph/0012127. doi:10.1109/18.985947. S2CID 523176.
Tropp, J. (2010). "User-friendly tail bounds for sums of random matrices". Foundations of Computational Mathematics. 12 (4): 389–434. arXiv:1004.4389. doi:10.1007/s10208-011-9099-z. S2CID 17735965.

web.archive.org

Wainwright, M. (January 22, 2015). "Basic tail and concentration bounds" (PDF). Archived (PDF) from the original on 2016-05-08.
Chernoff, Herman (2014). "A career in statistics" (PDF). In Lin, Xihong; Genest, Christian; Banks, David L.; Molenberghs, Geert; Scott, David W.; Wang, Jane-Ling (eds.). Past, Present, and Future of Statistics. CRC Press. p. 35. ISBN 9781482204964. Archived from the original (PDF) on 2015-02-11.
Sinclair, Alistair (Fall 2011). "Class notes for the course "Randomness and Computation"" (PDF). Archived from the original (PDF) on 31 October 2014. Retrieved 30 October 2014.

worldcat.org

Boucheron, Stéphane (2013). Concentration Inequalities: a Nonasymptotic Theory of Independence. Gábor Lugosi, Pascal Massart. Oxford: Oxford University Press. p. 21. ISBN 978-0-19-953525-5. OCLC 837517674.
Vershynin, Roman (2018). High-dimensional probability : an introduction with applications in data science. Cambridge, United Kingdom. p. 19. ISBN 978-1-108-41519-4. OCLC 1029247498.{{cite book}}: CS1 maint: location missing publisher (link)
Tropp, Joel A. (2015-05-26). "An Introduction to Matrix Concentration Inequalities". Foundations and Trends in Machine Learning. 8 (1–2): 60. arXiv:1501.01571. doi:10.1561/2200000048. ISSN 1935-8237. S2CID 5679583.
Chernoff, Herman (1952). "A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations". The Annals of Mathematical Statistics. 23 (4): 493–507. doi:10.1214/aoms/1177729330. ISSN 0003-4851. JSTOR 2236576.
Philips, Thomas K.; Nelson, Randolph (1995). "The Moment Bound Is Tighter Than Chernoff's Bound for Positive Tail Probabilities". The American Statistician. 49 (2): 175–178. doi:10.2307/2684633. ISSN 0003-1305. JSTOR 2684633.
Ghosh, Malay (2021-03-04). "Exponential Tail Bounds for Chisquared Random Variables". Journal of Statistical Theory and Practice. 15 (2): 35. doi:10.1007/s42519-020-00156-x. ISSN 1559-8616. S2CID 233546315.
Theodosopoulos, Ted (2007-03-01). "A reversion of the Chernoff bound". Statistics & Probability Letters. 77 (5): 558–565. arXiv:math/0501360. doi:10.1016/j.spl.2006.09.003. ISSN 0167-7152. S2CID 16139953.