메뉴 건너뛰기




Volumn 25, Issue 2, 2012, Pages 333-352

Approximation of Projections of Random Vectors

Author keywords

Entropy; Measure concentration; Projection pursuit; Random measures; Stein's method

Indexed keywords


EID: 79951845384     PISSN: 08949840     EISSN: 15729230     Source Type: Journal    
DOI: 10.1007/s10959-010-0299-2     Document Type: Article
Times cited : (26)

References (23)
  • 1
    • 0002005293 scopus 로고
    • Two moments suffice for Poisson approximations: the Chen-Stein method
    • Arratia, R., Goldstein, L., Gordon, L.: Two moments suffice for Poisson approximations: the Chen-Stein method. Ann. Probab. 17(1), 9-25 (1989).
    • (1989) Ann. Probab. , vol.17 , Issue.1 , pp. 9-25
    • Arratia, R.1    Goldstein, L.2    Gordon, L.3
  • 2
    • 84972496740 scopus 로고
    • Poisson approximation and the Chen-Stein method
    • With comments and a rejoinder by the authors
    • Arratia, R., Goldstein, L., Gordon, L.: Poisson approximation and the Chen-Stein method. Statist. Sci. 5(4), 403-434 (1990). With comments and a rejoinder by the authors.
    • (1990) Statist. Sci. , vol.5 , Issue.4 , pp. 403-434
    • Arratia, R.1    Goldstein, L.2    Gordon, L.3
  • 3
    • 0037248487 scopus 로고    scopus 로고
    • On concentration of distributions of random weighted sums
    • Bobkov, S. G.: On concentration of distributions of random weighted sums. Ann. Probab. 31(1), 195-215 (2003).
    • (2003) Ann. Probab. , vol.31 , Issue.1 , pp. 195-215
    • Bobkov, S.G.1
  • 4
    • 77049111151 scopus 로고    scopus 로고
    • Multivariate normal approximation using exchangeable pairs
    • Chatterjee, S., Meckes, E.: Multivariate normal approximation using exchangeable pairs. ALEA Lat. Am. J. Probab. Math. Stat. 4, 257-283 (2008).
    • (2008) ALEA Lat. Am. J. Probab. Math. Stat. , vol.4 , pp. 257-283
    • Chatterjee, S.1    Meckes, E.2
  • 5
    • 0001067389 scopus 로고
    • Poisson approximation for dependent trials
    • Chen, L. H. Y.: Poisson approximation for dependent trials. Ann. Probab. 3(3), 534-545 (1975).
    • (1975) Ann. Probab. , vol.3 , Issue.3 , pp. 534-545
    • Chen, L.H.Y.1
  • 6
    • 84860375503 scopus 로고    scopus 로고
    • Stein's method for Markov chains: first examples
    • IMS Lecture Notes Monogr. Ser, Beachwood: Inst. Math. Statist
    • Diaconis, P.: Stein's method for Markov chains: first examples. In: Stein's Method: Expository Lectures and Applications. IMS Lecture Notes Monogr. Ser., vol. 46, pp. 27-43. Inst. Math. Statist., Beachwood (2004).
    • (2004) Stein's Method: Expository Lectures and Applications , vol.46 , pp. 27-43
    • Diaconis, P.1
  • 7
    • 0001493668 scopus 로고
    • Asymptotics of graphical projection pursuit
    • Diaconis, P., Freedman, D.: Asymptotics of graphical projection pursuit. Ann. Stat. 12(3), 793-815 (1984).
    • (1984) Ann. Stat. , vol.12 , Issue.3 , pp. 793-815
    • Diaconis, P.1    Freedman, D.2
  • 8
    • 0000660999 scopus 로고
    • The sizes of compact subsets of Hilbert space and continuity of Gaussian processes
    • Dudley, R. M.: The sizes of compact subsets of Hilbert space and continuity of Gaussian processes. J. Funct. Anal. 1, 290-330 (1967).
    • (1967) J. Funct. Anal. , vol.1 , pp. 290-330
    • Dudley, R.M.1
  • 9
    • 0003418232 scopus 로고
    • Die Grundlehren der mathematischen Wissenschaften, New York: Springer
    • Federer, H.: Geometric Measure Theory. Die Grundlehren der mathematischen Wissenschaften, vol. 153, Springer, New York (1969).
    • (1969) Geometric Measure Theory , vol.153
    • Federer, H.1
  • 10
    • 85136412273 scopus 로고    scopus 로고
    • Limit theorems for spectra of random matrices with martingale structure
    • Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap, Singapore: Singapore Univ. Press
    • Götze, F., Tikhomirov, A. N.: Limit theorems for spectra of random matrices with martingale structure. In: Stein's Method and Applications. Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap., vol. 5, pp. 181-193. Singapore Univ. Press, Singapore (2005).
    • (2005) Stein's Method and Applications , vol.5 , pp. 181-193
    • Götze, F.1    Tikhomirov, A.N.2
  • 11
    • 33845508455 scopus 로고    scopus 로고
    • Stein's method for birth and death chains
    • IMS Lecture Notes Monogr. Ser, Beachwood, OH: Inst. Math. Statist
    • Holmes, S.: Stein's method for birth and death chains. In: Stein's Method: Expository Lectures and Applications. IMS Lecture Notes Monogr. Ser., vol. 46, pp. 45-67. Inst. Math. Statist., Beachwood, OH (2004).
    • (2004) Stein's Method: Expository Lectures and Applications , vol.46 , pp. 45-67
    • Holmes, S.1
  • 12
    • 0141987268 scopus 로고    scopus 로고
    • Classics in MathematicsDistribution theory and Fourier analysis, Reprint of the second (1990) edition [Springer, Berlin; MR1065993 (91m:35001a)], Berlin: Springer
    • Hörmander, L.: The Analysis of Linear Partial Differential Operators. I. Classics in Mathematics. Springer, Berlin (2003). Distribution theory and Fourier analysis, Reprint of the second (1990) edition [Springer, Berlin; MR1065993 (91m: 35001a)].
    • (2003) The Analysis of Linear Partial Differential Operators. I
    • Hörmander, L.1
  • 13
    • 0001467526 scopus 로고
    • Stein's method and multinomial approximation
    • Loh, W.-L.: Stein's method and multinomial approximation. Ann. Appl. Probab. 2(3), 536-554 (1992).
    • (1992) Ann. Appl. Probab. , vol.2 , Issue.3 , pp. 536-554
    • Loh, W.-L.1
  • 15
    • 85009755711 scopus 로고    scopus 로고
    • Quantitative asymptotics of graphical projection pursuit
    • Meckes, E. S.: Quantitative asymptotics of graphical projection pursuit. Electron. Commun. Probab. 14, 176-185 (2009).
    • (2009) Electron. Commun. Probab. , vol.14 , pp. 176-185
    • Meckes, E.S.1
  • 16
    • 79957949749 scopus 로고    scopus 로고
    • On Stein's method for multivariate normal approximation
    • IMS Coll, Beachwood: Inst. Math. Statist
    • Meckes, E.: On Stein's method for multivariate normal approximation. In: High Dimensional Probability V: The Luminy Volume. IMS Coll., vol. 5, pp. 153-178. Inst. Math. Statist., Beachwood (2009).
    • (2009) High Dimensional Probability V: The Luminy Volume , vol.5 , pp. 153-178
    • Meckes, E.1
  • 19
    • 77049095137 scopus 로고    scopus 로고
    • Multivariate normal approximation with Stein's method of exchangeable pairs under a general linearity condition
    • Reinert, G., Röllin, A.: Multivariate normal approximation with Stein's method of exchangeable pairs under a general linearity condition. Ann. Probab. 37(6), 2150-2173 (2009).
    • (2009) Ann. Probab. , vol.37 , Issue.6 , pp. 2150-2173
    • Reinert, G.1    Röllin, A.2
  • 21
    • 35549004360 scopus 로고
    • Typical distributions of linear functionals in finite-dimensional spaces of high dimension
    • Sudakov, V. N.: Typical distributions of linear functionals in finite-dimensional spaces of high dimension. Dokl. Akad. Nauk SSSR 243(6), 1402-1405 (1978).
    • (1978) Dokl. Akad. Nauk SSSR , vol.243 , Issue.6 , pp. 1402-1405
    • Sudakov, V.N.1
  • 23
    • 0040571285 scopus 로고    scopus 로고
    • Sudakov's typical marginals, random linear functionals and a conditional central limit theorem
    • von Weizsäcker, H.: Sudakov's typical marginals, random linear functionals and a conditional central limit theorem. Probab. Theory Relat. Fields 107(3), 313-324 (1997).
    • (1997) Probab. Theory Relat. Fields , vol.107 , Issue.3 , pp. 313-324
    • von Weizsäcker, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.