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Volumn , Issue , 2005, Pages 59-84

Stein’s method, Edgeworth’s expansions and a formula of Barbour

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EID: 77949570601     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/9789812567673_0004     Document Type: Chapter
Times cited : (8)

References (29)
  • 1
    • 0041566362 scopus 로고
    • Asymptotic expansions based on smooth functions in the central limit theorem
    • A. D. BARBOUR (1986) Asymptotic expansions based on smooth functions in the central limit theorem. Probab. Theory Rel. Fields 72, 289-303.
    • (1986) Probab. Theory Rel. Fields , vol.72 , pp. 289-303
    • Barbour, A.D.1
  • 4
    • 38249005717 scopus 로고
    • A central limit theorem for decomposable random variables with applications to random graphs
    • Ser. B
    • A. D. BARBOUR, M. KAROŃSKI and A. RUCIŃSKI (1989) A central limit theorem for decomposable random variables with applications to random graphs. J. Combin. Theory, Ser. B 47, 125-145.
    • (1989) J. Combin. Theory , vol.47 , pp. 125-145
    • Barbour, A.D.1    Karoński, M.2    Ruciński, A.3
  • 6
    • 0000390031 scopus 로고
    • Basic properties of strong mixing conditions. Dependence in probability and statistics
    • Oberwolfach, 1985, Birkhauser, Boston, Mass
    • R. C. BRADLEY (1985) Basic properties of strong mixing conditions. Dependence in probability and statistics. In: Progr. Probab. Statist. 11, (Oberwolfach, 1985), 165-192. Birkhauser, Boston, Mass.
    • (1985) Progr. Probab. Statist , vol.11 , pp. 165-192
    • Bradley, R.C.1
  • 7
    • 0032340621 scopus 로고    scopus 로고
    • On the simultaneous behavior of the dependence coefficients associated with three strong mixing conditions
    • R. C. BRADLEY (1998) On the simultaneous behavior of the dependence coefficients associated with three strong mixing conditions. Rocky Mountain J. Math. 28, 393-415.
    • (1998) Rocky Mountain J. Math , vol.28 , pp. 393-415
    • Bradley, R.C.1
  • 8
    • 0037718654 scopus 로고    scopus 로고
    • Volume 1. Technical Report, Department of Mathematics, Custom Publishing of IU, Indiana University, Bloomington
    • R. C. BRADLEY (2002) introduction to Strong Mixing Conditions, Volume 1. Technical Report, Department of Mathematics, Custom Publishing of IU, Indiana University, Bloomington.
    • (2002) Introduction to Strong Mixing Conditions
    • Bradley, R.C.1
  • 10
    • 0011228466 scopus 로고    scopus 로고
    • Stein’s method: Some perspectives with applications
    • Lecture Notes in Statistics 128, Springer, New York
    • L. H. Y. CHEN (1998) Stein’s method: some perspectives with applications. In: Probability towards 2000, Lecture Notes in Statistics 128, 97-122. Springer, New York.
    • (1998) Probability towards 2000 , pp. 97-122
    • Chen, L.H.Y.1
  • 11
    • 0000448413 scopus 로고
    • The invariance principle for stationary processes
    • Yu. A. DAVYDOV (1970) The invariance principle for stationary processes. Theor. Probab. Appl. 15, 487-498.
    • (1970) Theor. Probab. Appl , vol.15 , pp. 487-498
    • Davydov, Y.A.1
  • 12
    • 0000137215 scopus 로고
    • Mixing conditions for Markov chains
    • Yu. A. DAVYDOV (1973) Mixing conditions for Markov chains. Theor. Probab. Appl. 18, 312-328.
    • (1973) Theor. Probab. Appl , vol.18 , pp. 312-328
    • Davydov, Y.A.1
  • 13
    • 0040712215 scopus 로고    scopus 로고
    • Asymptotic distribution of quadratic forms
    • F. GÖTZE and A. N. TIKHOMIROV (1999) Asymptotic distribution of quadratic forms. Ann. Probab. 27, 1072-1098.
    • (1999) Ann. Probab , vol.27 , pp. 1072-1098
    • Götze, F.1    Tikhomirov, A.N.2
  • 14
    • 0036306670 scopus 로고    scopus 로고
    • Asymptotic distribution of quadratic forms and applications
    • F. GÖTZE and A. N. TIKHOMIROV (2002) Asymptotic distribution of quadratic forms and applications. J. Theoret. Probab. 15, 423-475.
    • (2002) J. Theoret. Probab , vol.15 , pp. 423-475
    • Götze, F.1    Tikhomirov, A.N.2
  • 15
    • 84890782483 scopus 로고
    • Spectral functions of certain classes of stationary Gaussian processes
    • I. A. IBRAGIMOV (1961) Spectral functions of certain classes of stationary Gaussian processes. Soviet Math. Dokl. 2, 403-405.
    • (1961) Soviet Math. Dokl , vol.2 , pp. 403-405
    • Ibragimov, I.A.1
  • 17
    • 84972578573 scopus 로고
    • Examples of mixing sequences
    • H. KESTEN and G. L. O’BRIEN (1976) Examples of mixing sequences. Duke Math. J. 43, 405-415.
    • (1976) Duke Math. J , vol.43 , pp. 405-415
    • Kesten, H.1    O’brien, G.L.2
  • 18
    • 0000803498 scopus 로고
    • On strong mixing conditions for stationary Gaussian processes
    • A. N. KOLMOGOROV and Yu. A. ROZANOV (1960) On strong mixing conditions for stationary Gaussian processes. Theor. Probab. Appl. 5, 204-208.
    • (1960) Theor. Probab. Appl , vol.5 , pp. 204-208
    • Kolmogorov, A.N.1    Rozanov, Y.A.2
  • 21
    • 33947358793 scopus 로고    scopus 로고
    • Couplings for normal approximations with Stein’s method
    • eds: D. J. Aldous and J. Propp, Dimacs series, AMS
    • G. REINERT (1998) Couplings for normal approximations with Stein’s method. In: Microsurveys in Discrete Probability, eds: D. J. Aldous and J. Propp. pp. 193-207. Dimacs series, AMS.
    • (1998) Microsurveys in Discrete Probability , pp. 193-207
    • Reinert, G.1
  • 22
    • 85136415407 scopus 로고    scopus 로고
    • An introduction to Stein’s method and application to empirical measures
    • eds: J. M. Gonzalez Barrios and L. G. Gorositza, Sociedad Matemätica Mexicana, Proceedings of the Symposium on Probability and Stochastic Processes, Guanajuato, Mexico
    • G. REINERT (1999) An introduction to Stein’s method and application to empirical measures. In: Modelos Estocästicos, eds: J. M. Gonzalez Barrios and L. G. Gorositza, Sociedad Matemätica Mexicana, pp. 65-120. Proceedings of the Symposium on Probability and Stochastic Processes, Guanajuato, Mexico.
    • (1999) Modelos Estocästicos , pp. 65-120
    • Reinert, G.1
  • 24
    • 0030075451 scopus 로고    scopus 로고
    • A multivariate CLT for local dependence with n-1/2logn rate, and applications to multivariate graph related statistics
    • Y. RINOTT and V. I. ROTAR (1996) A multivariate CLT for local dependence with n-1/2logn rate, and applications to multivariate graph related statistics. J. Multiv. Anal. 56, 333-350.
    • (1996) J. Multiv. Anal , vol.56 , pp. 333-350
    • Rinott, Y.1    Rotar, V.I.2
  • 26
    • 0042834085 scopus 로고    scopus 로고
    • On Edgeworth Expansions for Dependency- Neighborhoods Chain Structures and Stein’s Method
    • Y. RlNOTT and V. I. ROTAR (2003) On Edgeworth Expansions for Dependency- Neighborhoods Chain Structures and Stein’s Method. Probab. Theory Rel. Fields 126, 528-570.
    • (2003) Probab. Theory Rel. Fields , vol.126 , pp. 528-570
    • Rlnott, Y.1    Rotar, V.I.2
  • 27
    • 0000457248 scopus 로고
    • A bound for the error in the normal approximation to the distribution of a sum of dependent random variables
    • Univ. California Press, Berkeley
    • C. STEIN (1972) A bound for the error in the normal approximation to the distribution of a sum of dependent random variables. Proc. Sixth Berkeley Symp. Math. Statist. Prob. 2, pp. 583-602. Univ. California Press, Berkeley.
    • (1972) Proc. Sixth Berkeley Symp. Math. Statist. Prob , vol.2 , pp. 583-602
    • Stein, C.1
  • 29
    • 0001001924 scopus 로고
    • Convergence rate in the central limit theorem for weakly dependent random variables
    • A. N. TlKHOMIROV (1980) Convergence rate in the central limit theorem for weakly dependent random variables. Theor. Probab. Appl. 25, 800-818.
    • (1980) Theor. Probab. Appl , vol.25 , pp. 800-818
    • Tlkhomirov, A.N.1


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