메뉴 건너뛰기




Volumn 39, Issue 6, 2011, Pages 2318-2384

Uniform bounds for norms of sums of independent random functions

Author keywords

Concentration inequalities; Empirical processes; Kernel density estimation; Regression

Indexed keywords


EID: 84861404590     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/10-AOP595     Document Type: Article
Times cited : (17)

References (26)
  • 1
    • 0000356348 scopus 로고
    • Probability inequalities for empirical processes and a law of the iterated logarithm
    • MR0757769
    • Alexander, K. S. (1984). Probability inequalities for empirical processes and a law of the iterated logarithm. Ann. Probab. 12 1041-1067. MR0757769
    • (1984) Ann. Probab. , vol.12 , pp. 1041-1067
    • Alexander, K.S.1
  • 2
    • 0033459856 scopus 로고    scopus 로고
    • Risk bounds for model selection via penalization
    • MR1679028
    • Barron, A., Birgé, L. and Massart, P. (1999). Risk bounds for model selection via penalization. Probab. Theory Related Fields 113 301-413. MR1679028
    • (1999) Probab. Theory Related Fields , vol.113 , pp. 301-413
    • Barron, A.1    Birgé, L.2    Massart, P.3
  • 4
    • 0037561860 scopus 로고    scopus 로고
    • A Bennett concentration inequality and its application to suprema of empirical processes
    • MR1890640
    • Bousquet, O. (2002). A Bennett concentration inequality and its application to suprema of empirical processes. C. R. Math. Acad. Sci. Paris 334 495-500. MR1890640
    • (2002) C. R. Math. Acad. Sci. Paris , vol.334 , pp. 495-500
    • Bousquet, O.1
  • 5
    • 33845345610 scopus 로고    scopus 로고
    • Risk hull method and regularization by projections of ill-posed inverse problems
    • MR2283712
    • Cavalier, L. and Golubev, Y. (2006). Risk hull method and regularization by projections of ill-posed inverse problems. Ann. Statist. 34 1653-1677. MR2283712
    • (2006) Ann. Statist. , vol.34 , pp. 1653-1677
    • Cavalier, L.1    Golubev, Y.2
  • 7
    • 84865070319 scopus 로고    scopus 로고
    • Asymptotics of the rate of convergence for nonparametric density estimators: A new approach based on the Laplace method
    • MR1979745
    • Dümbgen, L. and Fatalov, V. R. (2002). Asymptotics of the rate of convergence for nonparametric density estimators: A new approach based on the Laplace method. Math. Methods Statist. 11 465-476 (2003). MR1979745
    • (2003) Math. Methods Statist. , vol.11 , pp. 465-476
    • Dümbgen, L.1    Fatalov, V.R.2
  • 8
    • 0034421301 scopus 로고    scopus 로고
    • An empirical process approach to the uniform consistency of kernel-type function estimators
    • MR1744994
    • Einmahl, U. and Mason, D. M. (2000). An empirical process approach to the uniform consistency of kernel-type function estimators. J. Theoret. Probab. 13 1-37. MR1744994
    • (2000) J. Theoret. Probab. , vol.13 , pp. 1-37
    • Einmahl, U.1    Mason, D.M.2
  • 10
    • 4544249147 scopus 로고    scopus 로고
    • Weighted uniform consistency of kernel density estimators
    • Giné, E., Koltchinskii, V. and Zinn, J. (2004). Weighted uniform consistency of kernel density estimators. Ann. Probab. 32 2570-2605. MR2078551
    • (2004) Ann. Probab. , vol.32 , pp. 2570-2605
    • Giné, E.1    Koltchinskii, V.2    Zinn, J.3
  • 11
    • 33746227538 scopus 로고    scopus 로고
    • Concentration inequalities and asymptotic results for ratio type empirical processes
    • MR2243881
    • Giné, E. and Koltchinskii, V. (2006). Concentration inequalities and asymptotic results for ratio type empirical processes. Ann. Probab. 34 1143-1216. MR2243881
    • (2006) Ann. Probab. , vol.34 , pp. 1143-1216
    • Giné, E.1    Koltchinskii, V.2
  • 13
    • 42149093784 scopus 로고    scopus 로고
    • Uniform central limit theorems for kernel density estimators
    • MR2391158
    • Giné, E. and Nickl, R. (2008). Uniform central limit theorems for kernel density estimators. Probab. Theory Related Fields 141 333-387. MR2391158
    • (2008) Theory Related Fields , vol.141 , pp. 333-387
    • Giné, E.1    Nickl, R.2
  • 14
    • 0000145024 scopus 로고
    • Some limit theorems for empirical processes
    • MR0757767
    • Giné, E. and Zinn, J. (1984). Some limit theorems for empirical processes. Ann. Probab. 12 929-998. MR0757767
    • (1984) Ann. Probab. , vol.12 , pp. 929-998
    • Giné, E.1    Zinn, J.2
  • 15
    • 58149352562 scopus 로고    scopus 로고
    • Universal pointwise selection rule in multivariate function estimation
    • MR2543590
    • Goldenshluger, A. and Lepski, O. (2008). Universal pointwise selection rule in multivariate function estimation. Bernoulli 14 1150-1190. MR2543590
    • (2008) Bernoulli , vol.14 , pp. 1150-1190
    • Goldenshluger, A.1    Lepski, O.2
  • 17
    • 85015983317 scopus 로고    scopus 로고
    • Exponential bounds for minimum contrast estimators
    • MR2534199
    • Golubev, Y. and Spokoiny, V. (2009). Exponential bounds for minimum contrast estimators. Electron. J. Statist. 3 712-746. MR2534199
    • (2009) Electron. J. Statist. , vol.3 , pp. 712-746
    • Golubev, Y.1    Spokoiny, V.2
  • 18
    • 0000537934 scopus 로고
    • Best constants in moment inequalities for linear combinations of independent and exchangeable random variables
    • MR0770640
    • Johnson, W.B., Schechtman, G. and Zinn, J. (1985). Best constants in moment inequalities for linear combinations of independent and exchangeable random variables. Ann. Probab. 13 234-253. MR0770640
    • (1985) Ann. Probab. , vol.13 , pp. 234-253
    • Johnson, W.B.1    Schechtman, G.2    Zinn, J.3
  • 20
    • 0034345597 scopus 로고    scopus 로고
    • About the constants in Talagrand's concentration inequalities for empirical processes
    • MR1782276
    • Massart, P. (2000). About the constants in Talagrand's concentration inequalities for empirical processes. Ann. Probab. 28 863-884. MR1782276
    • (2000) Ann. Probab. , vol.28 , pp. 863-884
    • Massart, P.1
  • 21
    • 0038095001 scopus 로고
    • Inequalities for distributions of the sums of independent random vectors and their application to the estimation of a density
    • MR1091221
    • Pinelis, I. F. (1990). Inequalities for distributions of the sums of independent random vectors and their application to the estimation of a density. Theory Probab. Appl. 35 605-607. MR1091221
    • (1990) Theory Probab. Appl. , vol.35 , pp. 605-607
    • Pinelis, I.F.1
  • 22
    • 0001638327 scopus 로고
    • Optimum bounds for the distributions of martingales in Banach spaces
    • MR1331198
    • Pinelis, I. (1994). Optimum bounds for the distributions of martingales in Banach spaces. Ann. Probab. 22 1679-1706. MR1331198
    • (1994) Ann. Probab. , vol.22 , pp. 1679-1706
    • Pinelis, I.1
  • 23
    • 0001957366 scopus 로고
    • Sharper bounds for Gaussian and empirical processes
    • MR1258865
    • Talagrand, M. (1994). Sharper bounds for Gaussian and empirical processes. Ann. Probab. 22 28-76. MR1258865
    • (1994) Ann. Probab. , vol.22 , pp. 28-76
    • Talagrand, M.1
  • 26
    • 0000095168 scopus 로고
    • Inequalities for the rth absolute moment of a sum of random variables, 1 ≤ r ≤ 2
    • MR0170407
    • Von Bahr, B. and Esseen, C.-G. (1965). Inequalities for the rth absolute moment of a sum of random variables, 1 ≤ r ≤ 2. Ann. Math. Statist. 36 299-303. MR0170407
    • (1965) Ann. Math. Statist. , vol.36 , pp. 299-303
    • Von Bahr, B.1    Esseen, C.-G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.