대한수학회지 (Journal of the Korean Mathematical Society)

  • 제51권1호
  • /
  • Pages.1-15
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  • 2014
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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CONDITIONAL CENTRAL LIMIT THEOREMS FOR A SEQUENCE OF CONDITIONAL INDEPENDENT RANDOM VARIABLES

  • Yuan, De-Mei (School of Mathematics and Statistics Chongqing Technology and Business University) ;
  • Wei, Li-Ran (College of Mathematics and Computer Science Yangtze Normal University) ;
  • Lei, Lan (School of Mathematics and Statistics Chongqing Technology and Business University)
  • 투고 : 2012.03.01
  • 발행 : 2014.01.01
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초록

A conditional version of the classical central limit theorem is derived rigorously by using conditional characteristic functions, and a more general version of conditional central limit theorem for the case of conditionally independent but not necessarily conditionally identically distributed random variables is established. These are done anticipating that the field of conditional limit theory will prove to be of significant applicability.

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참고문헌

  1. V. Basawa and B. L. S. Prakasa Rao, Statistical Inference for Stochastic Processes, London, Academic press, 1980.
  2. W. Grzenda and W.Zieba, Conditional central limit theorems, Int. Math. Forum 3 (2008), no. 29-32, 1521-1528.
  3. O. Kallenberg, Foundations of Modern Probability, 2nd Edition, Now York, Springer-Verlag, 2002.
  4. M. Loeve, Probability Theory II, 4th Edition, Now York, Springer-Verlag, 1978.
  5. D. Majerek, W. Nowak, and W. Zieba, Conditional strong law of large number, Int. J. Pure Appl. Math. 20 (2005), no. 2, 143-157.
  6. M. Ordonez Cabrera, A. Rosalsky, and A. Volodin, Some theorems on conditional mean convergence and conditional almost sure convergence for randomly weighted sums of dependent random variables, TEST 21 (2012), no. 2, 369-385. https://doi.org/10.1007/s11749-011-0248-0
  7. B. L. S. Prakasa Rao, Conditional independence, conditional mixing and conditional association, Ann. Inst. Statist. Math. 61 (2009), no. 2, 441-460. https://doi.org/10.1007/s10463-007-0152-2
  8. G. G. Roussas, On conditional independence, mixing, and association, Stoch. Anal. Appl. 26 (2008), no. 6, 1274-1309. https://doi.org/10.1080/07362990802405836
  9. A. N. Shiryaev, Probability, 2nd Edition, Now York, Springer-Verlag, 1995.
  10. D. M. Yuan, J. An, and X. S.Wu, Conditional limit theorems for conditionally negatively associated random variables, Monatsh. Math. 161 (2010), no. 4, 449-473. https://doi.org/10.1007/s00605-010-0196-x
  11. D. M. Yuan and L. Lei, Some conditional results for conditionally strong mixing sequences of random variables, Sci. China Math. 56 (2013), no. 4, 845-859. https://doi.org/10.1007/s11425-012-4554-0
  12. D. M. Yuan and Y. K. Yang, Conditional versions of limit theorems for conditionally associated random variables, J. Math. Anal. Appl. 376 (2011), no. 1, 282-293. https://doi.org/10.1016/j.jmaa.2010.10.046
  13. D. M. Yuan and Y. Xie, Conditional limit theorems for conditionally linearly negative quadrant dependent random variables, Monatsh. Math. 166 (2012), no. 2, 281-299. https://doi.org/10.1007/s00605-012-0373-1

피인용 문헌

  1. SOME RESULTS ON CONDITIONALLY UNIFORMLY STRONG MIXING SEQUENCES OF RANDOM VARIABLES vol.51, pp.3, 2014, https://doi.org/10.4134/JKMS.2014.51.3.609
  2. Modified first-difference estimator in a panel data model with unobservable factors both in the errors and the regressors when the time dimension is small 2017, https://doi.org/10.1080/03610926.2017.1295156
  3. Backward Mean-Field Linear-Quadratic-Gaussian (LQG) Games: Full and Partial Information vol.61, pp.12, 2016, https://doi.org/10.1109/TAC.2016.2519501
  4. A conditional version of the extended Kolmogorov–Feller weak law of large numbers vol.97, 2015, https://doi.org/10.1016/j.spl.2014.11.006
  5. A Conditional Approach to Panel Data Models with Common Shocks vol.4, pp.1, 2016, https://doi.org/10.3390/econometrics4010004
  6. The limit theorem for maximum of partial sums of exchangeable random variables vol.119, 2016, https://doi.org/10.1016/j.spl.2016.09.010
  7. Some results following from conditional characteristic functions vol.45, pp.12, 2016, https://doi.org/10.1080/03610926.2014.906614
  8. CONVERGENCE RATES FOR SEQUENCES OF CONDITIONALLY INDEPENDENT AND CONDITIONALLY IDENTICALLY DISTRIBUTED RANDOM VARIABLES vol.53, pp.6, 2016, https://doi.org/10.4134/JKMS.j150490
  9. Условная центральная предельная теорема vol.61, pp.4, 2016, https://doi.org/10.4213/tvp5083
  10. TSLS and LIML Estimators in Panels with Unobserved Shocks vol.6, pp.2, 2018, https://doi.org/10.3390/econometrics6020019