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Volumn 117, Issue 2, 2010, Pages 138-160

Nemirovski's inequalities revisited

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EID: 76749150068     PISSN: 00029890     EISSN: None     Source Type: Journal    
DOI: 10.4169/000298910X476059     Document Type: Article
Times cited : (37)

References (26)
  • 2
    • 0001917727 scopus 로고
    • Probability inequalities for the sum of independent random variables
    • doi:10.2307/2282438
    • G. Bennett, Probability inequalities for the sum of independent random variables, J. Amer. Statist. Assoc. 57 (1962) 33-45. doi:10.2307/2282438
    • (1962) J. Amer. Statist. Assoc. , vol.57 , pp. 33-45
    • Bennett, G.1
  • 4
    • 0003989054 scopus 로고    scopus 로고
    • Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge
    • R. M. Dudley, Uniform Central Limit Theorems, Cambridge Studies in Advanced Mathematics, vol.63, Cambridge University Press, Cambridge, 1999.
    • (1999) Uniform Central Limit Theorems , vol.63
    • Dudley, R.M.1
  • 5
    • 0000809561 scopus 로고
    • Central limit theorems and weak laws of large numbers in certain Banach spaces, Z
    • doi:10.1007/BF00535258
    • E. Giné and J. Zinn, Central limit theorems and weak laws of large numbers in certain Banach spaces, Z. Wahrsch. Verw. Gebiete 62 (1983) 323-354. doi:10.1007/BF00535258
    • (1983) Wahrsch. Verw. Gebiete , vol.62 , pp. 323-354
    • Giné, E.1    Zinn, J.2
  • 6
    • 0012850740 scopus 로고
    • Values of Mills' ratio of area to bounding ordinate and of the normal probability integral for large values of the argument
    • doi:10.1214/aoms/1177731721
    • R. D. Gordon, Values of Mills' ratio of area to bounding ordinate and of the normal probability integral for large values of the argument, Ann. Math. Statistics 12 (1941) 364-366. doi:10.1214/aoms/1177731721
    • (1941) Ann. Math. Statistics , vol.12 , pp. 364-366
    • Gordon, R.D.1
  • 7
    • 31344454903 scopus 로고    scopus 로고
    • Persistence in high-dimensional linear predictor selection and the virtue of overparametrization
    • doi:10.3150/bj/1106314846
    • E. Greenshtein and Y. Ritov, Persistence in high-dimensional linear predictor selection and the virtue of overparametrization, Bernoulli 10 (2004) 971-988. doi:10.3150/bj/1106314846
    • (2004) Bernoulli , vol.10 , pp. 971-988
    • Greenshtein, E.1    Ritov, Y.2
  • 8
    • 0001613468 scopus 로고
    • The best constants in the khintchine inequality
    • U. Haagerup, The best constants in the Khintchine inequality, Studia Math. 70 (1981) 231-283.
    • (1981) Studia Math. , vol.70 , pp. 231-283
    • Haagerup, U.1
  • 9
    • 84947403595 scopus 로고
    • Probability inequalities for sums of bounded random variables
    • doi:10.2307/2282952
    • W. Hoeffding, Probability inequalities for sums of bounded random variables, J. Amer. Statist. Assoc. 58 (1963) 13-30. doi:10.2307/2282952
    • (1963) J. Amer. Statist. Assoc. , vol.58 , pp. 13-30
    • Hoeffding, W.1
  • 11
    • 77956781055 scopus 로고    scopus 로고
    • Basic concepts in the geometry of Banach spaces
    • North-Holland, Amsterdam
    • W. B. Johnson and J. Lindenstrauss, Basic concepts in the geometry of Banach spaces, in Handbook of the Geometry of Banach Spaces, vol.1, North-Holland, Amsterdam, 2001, 1-84.
    • (2001) Handbook of the Geometry of Banach Spaces , vol.1 , pp. 1-84
    • Johnson, W.B.1    Lindenstrauss, J.2
  • 15
    • 76749125268 scopus 로고    scopus 로고
    • Regular Banach spaces and large deviations of random sums (working paper) 2004
    • Regular Banach spaces and large deviations of random sums (working paper) 2004.
  • 17
    • 10844254191 scopus 로고
    • 2 test under a symmetry condition
    • doi:10.1214/aos/1176325373
    • 2 test under a symmetry condition, Ann. Statist. 22 (1994) 357-368. doi:10.1214/aos/1176325373
    • (1994) Ann. Statist. , vol.22 , pp. 357-368
    • Pinelis, I.1
  • 18
    • 0001638327 scopus 로고
    • Optimum bounds for the distributions of martingales in Banach spaces
    • doi:10.1214/aop/1176988477
    • Optimum bounds for the distributions of martingales in Banach spaces, Ann. Probab. 22 (1994) 1679-1706. doi:10.1214/aop/1176988477
    • (1994) Ann. Probab. , vol.22 , pp. 1679-1706
  • 19
    • 27844498408 scopus 로고    scopus 로고
    • Monotonicity properties of the relative error of a Padé approximation for Mills' ratio
    • Monotonicity properties of the relative error of a Padé approximation for Mills' ratio, J. Inequal. Pure Appl. Math. 3/2 (2002).
    • (2002) J. Inequal. Pure Appl. Math. , vol.3 , Issue.2
  • 20
    • 84996139713 scopus 로고    scopus 로고
    • Toward the best constant factor for the Rademacher-Gaussian tail comparison
    • doi:10.1051/pa:2007027
    • Toward the best constant factor for the Rademacher-Gaussian tail comparison, ESAIM Probab. Stat. 11 (2007) 412-426. doi:10.1051/pa:2007027
    • (2007) ESAIM Probab. Stat. , vol.11 , pp. 412-426
  • 21
    • 76749143577 scopus 로고
    • NSF-CBMS Regional Conference Series in Probability and Statistics, 2, Institute of Mathematical Statistics, Hay ward, CA
    • D. Pollard, Empirical Processes: Theory and Applications, NSF-CBMS Regional Conference Series in Probability and Statistics, 2, Institute of Mathematical Statistics, Hay ward, CA, 1990.
    • (1990) Empirical Processes: Theory and Applications
    • Pollard, D.1
  • 22
    • 58549102501 scopus 로고    scopus 로고
    • Moment inequalities for sums of dependent random variables under projective conditions
    • doi:10.1007/s10959-008-0155-9
    • E. Rio, Moment inequalities for sums of dependent random variables under projective conditions, J. Theoret. Probab. 22(2009) 146-163. doi:10.1007/s10959-008-0155-9
    • (2009) J. Theoret. Probab. , vol.22 , pp. 146-163
    • Rio, E.1
  • 23
    • 0000395709 scopus 로고    scopus 로고
    • A nonsymmetric correlation inequality for Gaussian measure
    • doi:10.1006/jmva.1998.1784
    • S. J. Szarek and E. Werner, A nonsymmetric correlation inequality for Gaussian measure, J. Multivariate Anal. 68 (1999) 193-211.doi:10.1006/jmva.1998. 1784
    • (1999) J. Multivariate Anal. , vol.68 , pp. 193-211
    • Szarek, S.J.1    Werner, E.2
  • 24
    • 0003960026 scopus 로고
    • Pitman Monographs and Surveys in Pure and Applied Mathematics, Longman Scientific & Technical, Harlow, UK
    • N. Tomczak-Jægermann, Banach-Mazur Distances and Finite-Dimensional Operator Ideals, Pitman Monographs and Surveys in Pure and Applied Mathematics, vol.38, Longman Scientific & Technical, Harlow, UK, 1989.
    • (1989) Banach-Mazur Distances and Finite-Dimensional Operator Ideals , vol.38
    • Tomczak-Jægermann, N.1
  • 25
    • 0003885990 scopus 로고    scopus 로고
    • Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge University Press, Cambridge
    • S. A. van de Geer, Applications of Empirical Process Theory, Cambridge Series in Statistical and Probabilistic Mathematics, vol.6, Cambridge University Press, Cambridge, 2000.
    • (2000) Applications of Empirical Process Theory , vol.6
    • Van De Geer, S.A.1


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