메뉴 건너뛰기




Volumn 31, Issue 2, 2003, Pages 630-675

On extremal distributions and sharp Lp-bounds for sums of multilinear forms

Author keywords

Autocorrelation processes; Burkholder Rosenthal type and Khintchine type inequalities; Decoupling inequalities; Extremal distributions; Long range dependence; Moving average processes; Nonlinear statistics; Statistics; Sums of multilinear forms

Indexed keywords


EID: 18144451633     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1048516531     Document Type: Article
Times cited : (21)

References (45)
  • 2
    • 0002455942 scopus 로고
    • Distribution function inequalities for martingales
    • BURKHOLDER, D. L. (1973). Distribution function inequalities for martingales. Ann. Probab. 1 19-42.
    • (1973) Ann. Probab. , vol.1 , pp. 19-42
    • Burkholder, D.L.1
  • 3
    • 0000509434 scopus 로고
    • Decoupling and Khintchine's inequalities for U-statistics
    • DE LA PEÑA, V. H. (1992). Decoupling and Khintchine's inequalities for U-statistics. Ann. Probab. 20 1877-1892.
    • (1992) Ann. Probab. , vol.20 , pp. 1877-1892
    • De La Peña, V.H.1
  • 4
    • 0000566943 scopus 로고
    • Decoupling inequalities for the tail probabilities of multivariate U-statistics
    • DE LA PEÑA, V. H. and MONTGOMERY-SMITH, S. (1995). Decoupling inequalities for the tail probabilities of multivariate U-statistics. Ann. Probab. 23 806-816.
    • (1995) Ann. Probab. , vol.23 , pp. 806-816
    • De La Peña, V.H.1    Montgomery-Smith, S.2
  • 5
    • 0036542487 scopus 로고    scopus 로고
    • Decoupling and domination inequalities with application to Wald's identity for martingales
    • DE LA PEÑA, V. H. and ZAMFIRESCU, I.-M. (2002). Decoupling and domination inequalities with application to Wald's identity for martingales. Statist. Probab. Lett. 57 157-170.
    • (2002) Statist. Probab. Lett. , vol.57 , pp. 157-170
    • De La Peña, V.H.1    Zamfirescu, I.-M.2
  • 6
    • 21744443910 scopus 로고    scopus 로고
    • Extremal properties of Rademacher functions with applications to the Khintchine and Rosenthal inequalities
    • FIGIEL, T., HITCZENKO, P., JOHNSON, W. B., SCHECHTMAN, G. and ZINN, J. (1997). Extremal properties of Rademacher functions with applications to the Khintchine and Rosenthal inequalities. Trans. Amer. Math. Soc. 349 997-1027.
    • (1997) Trans. Amer. Math. Soc. , vol.349 , pp. 997-1027
    • Figiel, T.1    Hitczenko, P.2    Johnson, W.B.3    Schechtman, G.4    Zinn, J.5
  • 7
    • 0011321928 scopus 로고    scopus 로고
    • Exponential and moment inequalities for U-statistics
    • Birkhäuser, Boston
    • GINÉ, E., LATAŁA, R. and ZINN, J. (2000). Exponential and moment inequalities for U-statistics. In High-Dimensional Probability II 13-38. Birkhäuser, Boston.
    • (2000) High-Dimensional Probability II , pp. 13-38
    • Giné, E.1    Latała, R.2    Zinn, J.3
  • 8
    • 0001613468 scopus 로고
    • The best constants in the Khintchine inequality
    • HAAGERUP, U. (1982). The best constants in the Khintchine inequality. Studio Math. 70 231-283.
    • (1982) Studio Math. , vol.70 , pp. 231-283
    • Haagerup, U.1
  • 9
    • 0035627804 scopus 로고    scopus 로고
    • Limit theorems for the infinite-degree U-statistics
    • HEILIG, C. and NOLAN, D. (2001). Limit theorems for the infinite-degree U-statistics. Statist. Sinica 11 289-302.
    • (2001) Statist. Sinica , vol.11 , pp. 289-302
    • Heilig, C.1    Nolan, D.2
  • 10
    • 0000291602 scopus 로고
    • Best constants in martingale version of Rosenthal's inequality
    • HITCZENKO, P. (1990). Best constants in martingale version of Rosenthal's inequality. Ann. Probab. 18 1656-1668.
    • (1990) Ann. Probab. , vol.18 , pp. 1656-1668
    • Hitczenko, P.1
  • 11
    • 0001053569 scopus 로고
    • On a domination of sums of random variables by sums of conditionally independent ones
    • HITCZENKO, P. (1994a). On a domination of sums of random variables by sums of conditionally independent ones. Ann. Probab. 22 453-468.
    • (1994) Ann. Probab. , vol.22 , pp. 453-468
    • Hitczenko, P.1
  • 12
    • 84966231986 scopus 로고
    • On the behavior of the constant in a decoupling inequality for martingales
    • HITCZENKO, P. (1994b). On the behavior of the constant in a decoupling inequality for martingales. Proc. Amer. Math. Soc. 121 253-258.
    • (1994) Proc. Amer. Math. Soc. , vol.121 , pp. 253-258
    • Hitczenko, P.1
  • 13
    • 38149147764 scopus 로고
    • Sharp inequality for randomly stopped sums of independent nonnegative random variables
    • HITCZENKO, P. (1994c). Sharp inequality for randomly stopped sums of independent nonnegative random variables. Stochastic Process. Appl. 51 63-73.
    • (1994) Stochastic Process. Appl. , vol.51 , pp. 63-73
    • Hitczenko, P.1
  • 14
    • 0031325298 scopus 로고    scopus 로고
    • Limit theorems for functionals of moving averages
    • HO, H.-C. and HSING, T. (1997). Limit theorems for functionals of moving averages. Ann. Probab. 25 1636-1669.
    • (1997) Ann. Probab. , vol.25 , pp. 1636-1669
    • Ho, H.-C.1    Hsing, T.2
  • 17
    • 0000159623 scopus 로고    scopus 로고
    • On an exact constant for the Rosenthal inequality
    • [English translation in Theory Probab. Appl. 42 (1997) 294-302.]
    • IBRAGIMOV, R. and SHARAKHMETOV, SH. (1997). On an exact constant for the Rosenthal inequality. Teor. Veroyatnost. i Primen. 42 341-350. [English translation in Theory Probab. Appl. 42 (1997) 294-302.]
    • (1997) Teor. Veroyatnost. i Primen. , vol.42 , pp. 341-350
    • Ibragimov, R.1    Sharakhmetov, Sh.2
  • 19
    • 0033242705 scopus 로고    scopus 로고
    • Analogues of Khintchine, Marcinkiewicz-Zygmund and Rosenthal inequalities for symmetric statistics
    • IBRAGIMOV, R. and SHARAKHMETOV, SH. (1999). Analogues of Khintchine, Marcinkiewicz-Zygmund and Rosenthal inequalities for symmetric statistics. Scand. J. Statist. 26 621-623.
    • (1999) Scand. J. Statist. , vol.26 , pp. 621-623
    • Ibragimov, R.1    Sharakhmetov, Sh.2
  • 21
  • 22
    • 0000537934 scopus 로고
    • Best constants in moment inequalities for linear combinations of independent and exchangeable random variables
    • 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.
    • (1985) Ann. Probab. , vol.13 , pp. 234-253
    • Johnson, W.B.1    Schechtman, G.2    Zinn, J.3
  • 23
    • 0031477641 scopus 로고    scopus 로고
    • 2-functions of nonnegative random bilinear forms and generalized U-statistics
    • 2-functions of nonnegative random bilinear forms and generalized U-statistics. Ann. Probab. 25 1471-1501.
    • (1997) Ann. Probab. , vol.25 , pp. 1471-1501
    • Klass, M.J.1    Nowicki, K.2
  • 24
    • 0009319879 scopus 로고
    • Random multilinear forms
    • KRAKOWIAK, W. and SZULGA, J. (1986). Random multilinear forms. Ann. Probab. 14 955-973.
    • (1986) Ann. Probab. , vol.14 , pp. 955-973
    • Krakowiak, W.1    Szulga, J.2
  • 25
    • 0011409278 scopus 로고
    • Hypercontraction methods in moment inequalities for series of independent random variables in normed spaces
    • KWAPIEŃ, S. and SZULGA, J. (1991). Hypercontraction methods in moment inequalities for series of independent random variables in normed spaces. Ann. Probab. 19 1-8.
    • (1991) Ann. Probab. , vol.19 , pp. 1-8
    • Kwapień, S.1    Szulga, J.2
  • 27
    • 0041157299 scopus 로고    scopus 로고
    • Estimation of moments of sums of independent real random variables
    • LATAŁA, R. (1997). Estimation of moments of sums of independent real random variables. Ann. Probab. 25 1502-1513.
    • (1997) Ann. Probab. , vol.25 , pp. 1502-1513
    • Latała, R.1
  • 28
    • 0003256486 scopus 로고
    • Inequalities: Theory of majorization and its applications
    • MARSHALL, A. W. and OLKIN, I. (1979). Inequalities: Theory of majorization and its applications. Math. Sci. Engrg. 143.
    • (1979) Math. Sci. Engrg. , vol.143
    • Marshall, A.W.1    Olkin, I.2
  • 29
    • 0000000103 scopus 로고
    • Decoupling inequalities for multilinear forms in independent symmetric random variables
    • McCONNELL, T. R. and TAQQU, M. (1986). Decoupling inequalities for multilinear forms in independent symmetric random variables. Ann. Probab. 14 943-954.
    • (1986) Ann. Probab. , vol.14 , pp. 943-954
    • McConnell, T.R.1    Taqqu, M.2
  • 30
    • 0001581028 scopus 로고
    • On a new approach to the study of the distribution of a norm of a random element in Hilbert space
    • Mokslas, Vilnius
    • NAGAEV, S. V. (1990). On a new approach to the study of the distribution of a norm of a random element in Hilbert space. In Probability Theory and Mathematical Statistics 2 214-226. Mokslas, Vilnius.
    • (1990) Probability Theory and Mathematical Statistics , vol.2 , pp. 214-226
    • Nagaev, S.V.1
  • 31
    • 0031291895 scopus 로고    scopus 로고
    • Some refinements of probabilistic and moment inequalities
    • NAGAEV, S. V. (1998). Some refinements of probabilistic and moment inequalities. Theory Probab. Appl. 42 707-713.
    • (1998) Theory Probab. Appl. , vol.42 , pp. 707-713
    • Nagaev, S.V.1
  • 32
    • 0000143520 scopus 로고
    • Some inequalities for the distributions of sums of independent random variables
    • NAGAEV, S. V. and PINELIS, I. F. (1977). Some inequalities for the distributions of sums of independent random variables. Theory Probab. Appl. 22 248-256.
    • (1977) Theory Probab. Appl. , vol.22 , pp. 248-256
    • Nagaev, S.V.1    Pinelis, I.F.2
  • 33
    • 84923132097 scopus 로고
    • Khinchin inequalities and a martingale extension of the sphere of their action
    • PESHKIR, G. and SHIRYAEV, A. N. (1995). Khinchin inequalities and a martingale extension of the sphere of their action. Russian Math. Surveys 50 849-904.
    • (1995) Russian Math. Surveys , vol.50 , pp. 849-904
    • Peshkir, G.1    Shiryaev, A.N.2
  • 34
    • 0010006651 scopus 로고
    • Estimates for moments of infinite-dimensional martingales
    • PINELIS, I. F. (1980). Estimates for moments of infinite-dimensional martingales. Math. Notes 27 459-462.
    • (1980) Math. Notes , vol.27 , pp. 459-462
    • Pinelis, I.F.1
  • 35
    • 0001638327 scopus 로고
    • Optimum bounds for the distributions of martingales in Banach spaces
    • PINELIS, I. (1994). Optimum bounds for the distributions of martingales in Banach spaces. Ann. Probab. 22 1679-1706.
    • (1994) Ann. Probab. , vol.22 , pp. 1679-1706
    • Pinelis, I.1
  • 36
    • 0001508060 scopus 로고
    • Estimates of moments of sums of independent random variables
    • PINELIS, I. F. and UTEV, S. A. (1984). Estimates of moments of sums of independent random variables. Theory Probab. Appl. 29 574-577.
    • (1984) Theory Probab. Appl. , vol.29 , pp. 574-577
    • Pinelis, I.F.1    Utev, S.A.2
  • 37
    • 51249187914 scopus 로고
    • p (p > 2) spanned by sequences of independent random variables
    • p (p > 2) spanned by sequences of independent random variables. Israel J. Math. 8 273-303.
    • (1970) Israel J. Math. , vol.8 , pp. 273-303
    • Rosenthal, H.P.1
  • 38
    • 0003573386 scopus 로고    scopus 로고
    • Combinatorial methods in discrete mathematics
    • SACHKOV, V. N. (1996). Combinatorial methods in discrete mathematics. Encyclopedia Math. Appl. 55.
    • (1996) Encyclopedia Math. Appl. , vol.55
    • Sachkov, V.N.1
  • 39
    • 0009998830 scopus 로고
    • On the estimation of moments of sums of independent random variables
    • SAZONOV, V. V. (1974). On the estimation of moments of sums of independent random variables. Theory Probab. Appl. 19 371-374.
    • (1974) Theory Probab. Appl. , vol.19 , pp. 371-374
    • Sazonov, V.V.1
  • 42
    • 0000228838 scopus 로고
    • Isoperimetry and integrability of the sum of independent Banach-space valued random variables
    • TALAGRAND, M. (1989). Isoperimetry and integrability of the sum of independent Banach-space valued random variables. Ann. Probab. 17 1546-1570.
    • (1989) Ann. Probab. , vol.17 , pp. 1546-1570
    • Talagrand, M.1
  • 44
    • 0012930683 scopus 로고
    • Sharp inequalities for the conditional square function of a martingale
    • WANG, G. (1991a). Sharp inequalities for the conditional square function of a martingale. Ann. Probab. 19 1679-1688.
    • (1991) Ann. Probab. , vol.19 , pp. 1679-1688
    • Wang, G.1
  • 45
    • 84966248196 scopus 로고
    • Sharp square-function inequalities for conditionally symmetric martingales
    • WANG, G. (1991b). Sharp square-function inequalities for conditionally symmetric martingales. Trans. Amer. Math. Soc. 328 393-419.
    • (1991) Trans. Amer. Math. Soc. , vol.328 , pp. 393-419
    • Wang, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.