Conditional central limit theorems for a sequence of conditional independent random variables
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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.
Abstract
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.
참고문헌 (13)
- V. Basawa, "Statistical Inference for Stochastic Processes" (1980), Academic press
- W. Grzenda, "Conditional central limit theorems", Int. Math. Forum, 3(29-32), pp.1521~1528 (2008)
- O. Kallenberg, "Foundations of Modern Probability" (2002), Springer-Verlag
- M. Loeve, "Probability Theory II" (1978), Springer-Verlag
- D. Majerek, "Conditional strong law of large number", Int. J. Pure Appl. Math, 20(2), pp.143~157 (2005)
- M. Ordonez Cabrera, "Some theorems on conditional mean convergence and conditional almost sure convergence for randomly weighted sums of dependent random variables", TEST, 21(2), pp.369~385 (2012)
- B. L. S. Prakasa Rao, "Conditional independence, conditional mixing and conditional association", Ann. Inst. Statist. Math, 61(2), pp.441~460 (2009)
- G. G. Roussas, "On conditional independence, mixing, and association", Stoch. Anal. Appl, 26(6), pp.1274~1309 (2008)
- A. N. Shiryaev, "Probability" (1995), Springer-Verlag
- D. M. Yuan, "Conditional limit theorems for conditionally negatively associated random variables", Monatsh. Math, 161(4), pp.449~473 (2010)
- D. M. Yuan, "Some conditional results for conditionally strong mixing sequences of random variables", Sci. China Math, 56(4), pp.845~859 (2013)
- D. M. Yuan, "Conditional versions of limit theorems for conditionally associated random variables", J. Math. Anal. Appl, 376(1), pp.282~293 (2011)
- D. M. Yuan, "Conditional limit theorems for conditionally linearly negative quadrant dependent random variables", Monatsh. Math, 166(2), pp.281~299 (2012)
