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Volumn , Issue , 2000, Pages 87-100

Unified variance bounds and a stein-type identity

Author keywords

Stein type identity; Transformation of random variables; Variance bounds

Indexed keywords


EID: 84962022819     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Chapter
Times cited : (10)

References (18)
  • 1
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    • Cacoullos, T. (1982). On upper and lower bounds for the variance of a function of a random variable. Annals of Probability10, 799-809.
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    • Cacoullos, T.1
  • 3
    • 0000376895 scopus 로고
    • On upper bounds for the variance of functions of random variables
    • Cacoullos, T. and Papathanasiou, V. (1985). On upper bounds for the variance of functions of random variables. Statistics & Probability Letters3, 175-184.
    • (1985) Statistics & Probability Letters , vol.3 , pp. 175-184
    • Cacoullos, T.1    Papathanasiou, V.2
  • 5
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    • A generalization of covariance identity and related characterizations
    • Cacoullos, T. and Papathanasiou, V. (1995). A generalization of covariance identity and related characterizations. Mathematical Methods of Statistics 4, 106-113.
    • (1995) Mathematical Methods of Statistics , vol.4 , pp. 106-113
    • Cacoullos, T.1    Papathanasiou, V.2
  • 6
    • 0000369910 scopus 로고
    • Another characterization of the normal law and a proof of the central limit theorem connected with it
    • (in Russian)
    • Cacoullos, T., Papathanasiou, V., and Utev, S. (1992). Another characterization of the normal law and a proof of the central limit theorem connected with it. Theory of Probability and its Applications37, 648-657 (in Russian).
    • (1992) Theory of Probability and Its Applications , vol.37 , pp. 648-657
    • Cacoullos, T.1    Papathanasiou, V.2    Utev, S.3
  • 7
    • 0000985130 scopus 로고
    • Variational inequalities with examples and an application to the central limit theorem
    • Cacoullos, T., Papathanasiou, V., and Utev, S. (1994). Variational inequalities with examples and an application to the central limit theorem. Annals of Probability22, 1607-1618.
    • (1994) Annals of Probability , vol.22 , pp. 1607-1618
    • Cacoullos, T.1    Papathanasiou, V.2    Utev, S.3
  • 8
    • 0000623383 scopus 로고
    • An inequality for the multivariate normal distribution
    • Chen, L. H. Y. (1982). An inequality for the multivariate normal distribution. Journal of Multivariate Analysis12, 306-315.
    • (1982) Journal of Multivariate Analysis , vol.12 , pp. 306-315
    • Chen, L.H.Y.1
  • 9
    • 0000784286 scopus 로고
    • The central limit theorem and Poincare type inequalities
    • Chen, L. H. Y. (1988). The central limit theorem and Poincare type inequalities. Annals of Probability16, 300-304.
    • (1988) Annals of Probability , vol.16 , pp. 300-304
    • Chen, L.H.Y.1
  • 10
    • 0001136294 scopus 로고
    • A note on an inequality involving the normal distribution
    • Chernoff, H. (1981). A note on an inequality involving the normal distribution. Annals of Probability 9, 533-535.
    • (1981) Annals of Probability , vol.9 , pp. 533-535
    • Chernoff, H.1
  • 11
    • 0031260681 scopus 로고    scopus 로고
    • Stein’s method and the Zero Bias Transformation with application to simple random sampling
    • Goldstein, L. and Reinert, G. (1997). Stein’s method and the Zero Bias Transformation with application to simple random sampling. Annals of Applied Probability7, 935-952.
    • (1997) Annals of Applied Probability , vol.7 , pp. 935-952
    • Goldstein, L.1    Reinert, G.2
  • 12
    • 0001430370 scopus 로고
    • A natural identity for exponential families with applications to multiparameter estimation
    • Hudson, H. M. (1978). A natural identity for exponential families with applications to multiparameter estimation. Annals of Statistics6, 473-484.
    • (1978) Annals of Statistics , vol.6 , pp. 473-484
    • Hudson, H.M.1
  • 13
    • 0012042987 scopus 로고
    • Siegel’s formula via Stein’s identities
    • Liu, J. S. (1994). Siegel’s formula via Stein’s identities. Statistics & Probability Letters21, 247-251.
    • (1994) Statistics & Probability Letters , vol.21 , pp. 247-251
    • Liu, J.S.1
  • 14
    • 38249017611 scopus 로고
    • Characterizations of multidimensional exponential families by Cacoullos-type inequalities
    • Papathanasiou, V. (1990). Characterizations of multidimensional exponential families by Cacoullos-type inequalities. Journal of Multivariate Analysis35, 102-107.
    • (1990) Journal of Multivariate Analysis , vol.35 , pp. 102-107
    • Papathanasiou, V.1
  • 15
    • 0000430373 scopus 로고
    • Some characteristic properties of the Fisher information matrix via Cacoullos-type inequalities
    • Papathanasiou, V. (1993). Some characteristic properties of the Fisher information matrix via Cacoullos-type inequalities. Journal of Multivariate Analysis44, 256-265.
    • (1993) Journal of Multivariate Analysis , vol.44 , pp. 256-265
    • Papathanasiou, V.1
  • 16
    • 0000457248 scopus 로고
    • A bound for the error in the normal approximation to the distribution of a sum of dependent random variables
    • University California Press, Berkeley
    • Stein, C. (1972). A bound for the error in the normal approximation to the distribution of a sum of dependent random variables. In Proceedings of the Sixth Berkeley Symposium on Mathematics, Statistics and Probability2, 583-602. University California Press, Berkeley.
    • (1972) Proceedings of the Sixth Berkeley Symposium on Mathematics, Statistics and Probability , vol.2 , pp. 583-602
    • Stein, C.1
  • 17
    • 0000169918 scopus 로고
    • Estimation of the mean of a multivariate normal distribution
    • Stein, C. (1981). Estimation of the mean of a multivariate normal distribution. Annals of Statistics9, 1135-1151.
    • (1981) Annals of Statistics , vol.9 , pp. 1135-1151
    • Stein, C.1
  • 18
    • 38249027824 scopus 로고
    • A differential version of the Efron-Stein inequality: Bounding the varianee of an infinitely divisible variable
    • Vitale, R. A. (1989). A differential version of the Efron-Stein inequality: Bounding the varianee of an infinitely divisible variable. Statistics & Probability Letters7, 105-112.
    • (1989) Statistics & Probability Letters , vol.7 , pp. 105-112
    • Vitale, R.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.