메뉴 건너뛰기




Volumn 37, Issue 6, 2009, Pages 2150-2173

Multivariate normal approximation with stein's method of exchangeable pairs under a general linearity condition

Author keywords

Exchangeable pairs; Multivariate normal approximation; Stein's method

Indexed keywords


EID: 77049095137     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/09-AOP467     Document Type: Article
Times cited : (149)

References (29)
  • 2
    • 0000499854 scopus 로고
    • Stein's method for diffusion approximations
    • Barbour, A. D. (1990). Stein's method for diffusion approximations. Probab. Theory Related Fields 84 297-322.
    • (1990) Probab. Theory Related Fields , vol.84 , pp. 297-322
    • Barbour, A.D.1
  • 3
    • 84918528157 scopus 로고    scopus 로고
    • The permutation distribution of matrix correlation statistics In Stein's Method and Applications
    • Singapore Univ. Press, Singapore
    • Barbour, A.D. and Chen, L. H. Y. (2005). The permutation distribution of matrix correlation statistics. In Stein's Method and Applications. Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap. 5 223-245. Singapore Univ. Press, Singapore.
    • (2005) Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap. , vol.5 , pp. 223-245
    • Barbour, A.D.1    Chen, L.H.Y.2
  • 5
    • 0000817812 scopus 로고
    • An estimate of the remainder in a combinatorial central limit theorem
    • Bolthausen, E. (1984). An estimate of the remainder in a combinatorial central limit theorem. Z. Wahrsch. Verw. Gebiete 66 379-386.
    • (1984) Z. Wahrsch. Verw. Gebiete , vol.66 , pp. 379-386
    • Bolthausen, E.1
  • 6
    • 21344480022 scopus 로고
    • The rate of convergence for multivariate sampling statistics
    • Bolthausen, E. and Götze, F. (1993). The rate of convergence for multivariate sampling statistics. Ann. Statist. 21 1692-1710.
    • (1993) Ann. Statist. , vol.21 , pp. 1692-1710
    • Bolthausen, E.1    Götze, F.2
  • 7
    • 52049105232 scopus 로고    scopus 로고
    • Exponential approximation by exchangeable pairs and spectral graph theory
    • Preprint. Available at
    • Chatterjee, S., Fulman, J. and Röllin, A. (2006). Exponential approximation by exchangeable pairs and spectral graph theory. Preprint. Available at www.arxiv.org/math.PR/0605552.
    • (2006)
    • Chatterjee, S.1    Fulman, J.2    Röllin, A.3
  • 8
    • 77049111151 scopus 로고    scopus 로고
    • Multivariate normal approximation using exchangeable pairs ALEA Lat
    • Chatterjee, S. and Meckes, E. (2008). Multivariate normal approximation using exchangeable pairs. ALEA Lat. Am. J. Probab. Math. Stat. 4 257-283.
    • (2008) ALEA Lat. Am. J. Probab. Math. Stat. , vol.4 , pp. 257-283
    • Chatterjee, S.1    Meckes, E.2
  • 9
    • 23244451108 scopus 로고    scopus 로고
    • Exchangeable pairs and Poisson approximation
    • (electronic)
    • Chatterjee, S., Diaconis, P. and Meckes, E. (2005). Exchangeable pairs and Poisson approximation. Probab. Surv. 2 64-106 (electronic).
    • (2005) Probab. Surv. , vol.2 , pp. 64-106
    • Chatterjee, S.1    Diaconis, P.2    Meckes, E.3
  • 10
    • 12744250791 scopus 로고    scopus 로고
    • Stein's method and non-reversible Markov chains
    • (P. Diaconis and S. Holmes, eds.) IMS, Beachwood, OH
    • Fulman, J. (2004). Stein's method and non-reversible Markov chains. In Stein's Method: Exposi tory Lectures and Applications (P. Diaconis and S. Holmes, eds.) 69-77. IMS, Beachwood, OH.
    • (2004) Stein's Method: Exposi tory Lectures and Applications , pp. 69-77
    • Fulman, J.1
  • 12
    • 84971351293 scopus 로고    scopus 로고
    • Zero biasing in one and higher dimensions, and applica tions In Stein's Method and Applications
    • Singapore Univ. Press, Singapore
    • Goldstein, L. and Reinert, G. (2005). Zero biasing in one and higher dimensions, and applica tions. In Stein's Method and Applications. Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap. 5 1-18. Singapore Univ. Press, Singapore.
    • (2005) Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap. , vol.5 , pp. 1-18
    • Goldstein, L.1    Reinert, G.2
  • 13
    • 0030535645 scopus 로고    scopus 로고
    • Multivariate normal approximations by Stein's method and size bias couplings
    • Goldstein, L. and Rinott, Y. (1996). Multivariate normal approximations by Stein's method and size bias couplings. J. Appl. Probab. 33 1-17.
    • (1996) J. Appl. Probab. , vol.33 , pp. 1-17
    • Goldstein, L.1    Rinott, Y.2
  • 14
    • 0001354702 scopus 로고
    • On the rate of convergence in the multivariate CLT
    • Götze, F. (1991). On the rate of convergence in the multivariate CLT. Ann. Probab. 19 724-739.
    • (1991) Ann. Probab. , vol.19 , pp. 724-739
    • Götze, F.1
  • 15
    • 0000680233 scopus 로고
    • A combinatorial central limit theorem
    • Hoeffding, W. (1951). A combinatorial central limit theorem. Ann. Math. Statist. 22 558-566.
    • (1951) Ann. Math. Statist. , vol.22 , pp. 558-566
    • Hoeffding, W.1
  • 16
    • 0012063617 scopus 로고
    • Bounds for condition numbers of triangular and trapezoid matrices
    • Lemeire, F. (1975). Bounds for condition numbers of triangular and trapezoid matrices. Nordisk Tidskr. Informationsbehandling (BIT) 15 58-64.
    • (1975) Nordisk Tidskr. Informationsbehandling (BIT) , vol.15 , pp. 58-64
    • Lemeire, F.1
  • 17
    • 51049091711 scopus 로고    scopus 로고
    • A multivariate central limit theorem for randomized orthogonal array sampling designs in computer experiments
    • Loh, W.-L. (2008). A multivariate central limit theorem for randomized orthogonal array sampling designs in computer experiments. Ann. Statist. 36 1983-2023.
    • (2008) Ann. Statist. , vol.36 , pp. 1983-2023
    • Loh, W.-L.1
  • 18
    • 0002322469 scopus 로고
    • On a test of whether one of two random variables is stochastically larger than the other
    • Mann, H.B.and Whitney, D. R. (1947). On a test of whether one of two random variables is stochastically larger than the other. Ann. Math. Statist. 18 50-60.
    • (1947) Ann. Math. Statist. , vol.18 , pp. 50-60
    • Mann, H.B.1    Whitney, D.R.2
  • 20
    • 4544380832 scopus 로고    scopus 로고
    • A multivariate CLT for decomposable random vectors with finite second moments
    • Raič, M. (2004). A multivariate CLT for decomposable random vectors with finite second moments. J. Theoret. Probab. 17 573-603.
    • (2004) J. Theoret. Probab. , vol.17 , pp. 573-603
    • Raič, M.1
  • 21
    • 67349131956 scopus 로고    scopus 로고
    • Three general approaches to Stein's method In An Introduction to Stein's Method
    • Singapore Univ. Press, Singapore
    • Reinert, G. (2005). Three general approaches to Stein's method. In An Introduction to Stein's Method. Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap. 4 183-221. Singapore Univ. Press, Singapore.
    • (2005) Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap. , vol.4 , pp. 183-221
    • Reinert, G.1
  • 22
    • 0030075451 scopus 로고    scopus 로고
    • -1/2 log n rate and applications to multivariate graph related statistics
    • -1/2 log n rate and applications to multivariate graph related statistics. J. Multivariate Anal. 56 333-350.
    • (1996) J. Multivariate Anal. , vol.56 , pp. 333-350
    • Rinott, Y.1    Rotar, V.2
  • 23
    • 0031260684 scopus 로고    scopus 로고
    • On coupling constructions and rates in the CLT for dependent summands with applications to the antivoter model and weighted U-statistics
    • Rinott, Y. and Rotar, V. (1997). On coupling constructions and rates in the CLT for dependent summands with applications to the antivoter model and weighted U-statistics. Ann. Appl. Probab. 7 1080-1105.
    • (1997) Ann. Appl. Probab. , vol.7 , pp. 1080-1105
    • Rinott, Y.1    Rotar, V.2
  • 24
    • 49649109655 scopus 로고    scopus 로고
    • Translated Poisson approximation using exchangeable pair couplings
    • Röllin, A. (2007). Translated Poisson approximation using exchangeable pair couplings. Ann. Appl. Probab. 17 1596-1614.
    • (2007) Ann. Appl. Probab. , vol.17 , pp. 1596-1614
    • Röllin, A.1
  • 25
    • 49649090689 scopus 로고    scopus 로고
    • A note on the exchangeability condition in Stein's method
    • Röllin, A. (2008). A note on the exchangeability condition in Stein's method. Statist. Probab. Lett. 78 1800-1806.
    • (2008) Statist. Probab. Lett. , vol.78 , pp. 1800-1806
    • Röllin, A.1
  • 26
    • 0004269085 scopus 로고    scopus 로고
    • World Scientific, River Edge, NJ
    • Rotar, V. (1997). Probability Theory. World Scientific, River Edge, NJ.
    • (1997) Probability Theory
    • Rotar, V.1
  • 27
    • 0000457248 scopus 로고
    • A bound for the error in the normal approximation to the distribution of a sum of dependent random variables
    • Probability Theory. Univ. California Press, Berkeley, CA.
    • Stein, C. (1972). A bound for the error in the normal approximation to the distribution of a sum of dependent random variables. In Proc. Sixth Berkeley Symp. Math. Statist. Probab. Vol. II: Probability Theory. Univ. California Press, Berkeley, CA.
    • (1972) Proc. Sixth Berkeley Symp. Math. Statist. Probab. , vol.2
    • Stein, C.1
  • 29
    • 0031505974 scopus 로고    scopus 로고
    • Error bound in a central limit theorem of double-indexed permutation statistics
    • Zhao, L., Bai, Z., Chao, C.-C.and Liang, W.-Q. (1997). Error bound in a central limit theorem of double-indexed permutation statistics. Ann. Statist. 25 2210-2227.
    • (1997) Ann. Statist. , vol.25 , pp. 2210-2227
    • Zhao, L.1    Bai, Z.2    Chao, C.-C.3    Liang, W.-Q.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.