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Central limit theorems for conditionally strong mixing and conditionally strictly stationary sequences of random variables

De-Mei Yuan|Xiao-Lin Zeng
대한수학회 (The Korean Mathematical Society)|2024.07|대한수학회지 (Journal of the KMS)|제61권 제4호|pp. 713-742|DOI 10.4134/JKMS.j230332

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참고문헌

키워드

Strong mixingconditionally strong mixingconditionally upper-tail quantile functionconditional stationarityconditional central limit theorem
주제분류수학

초록

From the ordinary notion of upper-tail quantitle function, a new concept called conditionally upper-tail quantitle function given a $\sigma$-algebra is proposed. Some basic properties of this terminology and further properties of conditionally strictly stationary sequences are derived. By means of these properties, several conditional central limit theorems for a sequence of conditionally strong mixing and conditionally strictly stationary random variables are established, some of which are the conditional versions corresponding to earlier results under non-conditional case.

Abstract

From the ordinary notion of upper-tail quantitle function, a new concept called conditionally upper-tail quantitle function given a $\sigma$-algebra is proposed. Some basic properties of this terminology and further properties of conditionally strictly stationary sequences are derived. By means of these properties, several conditional central limit theorems for a sequence of conditionally strong mixing and conditionally strictly stationary random variables are established, some of which are the conditional versions corresponding to earlier results under non-conditional case.

참고문헌 (27)

  1. R. C. Bradley Jr., "Introduction to Strong Mixing Conditions Vol. 1" (2007), Kendrick Press
  2. W. Bryc, "Large deviations and strong mixing", Ann. Inst. H. Poincar´e Probab. Statist, 32(4), pp.549~569 (1996)
  3. A. V. Bulinski, "Conditional central limit theorem", Theory Probab. Appl, 61(4), pp.686~708 (2016)[DOI]
  4. T. C. Christofides, "The conditional convex order and a comparison inequality", Stoch. Anal. Appl, 33(2), pp.259~270 (2015)[DOI]
  5. D. D. Cox, "Moment bounds for mixing random variables useful in nonparametric function estimation", Stoch. Process. their Appl, 56(1), pp.151~158 (1995)[DOI]
  6. M. Ekstrom, "A general central limit theorem for strong mixing sequences", Statist. Probab. Lett, 94, pp.236~238 (2014)[DOI]
  7. S. Khovansky, "On the consistency of a cross-sectional GMM estimator in the presence of an observable stochastic common data shock", Statist. Probab. Lett, 129, pp.196~202 (2017)[DOI]
  8. J. H. Lee, "Stable limit theorems for empirical processes under conditional neighborhood dependence", Bernoulli, 25(2), pp.1189~1224 (2019)[DOI]
  9. F. Merlevade, "The functional central limit theorem under the strong mixing condition", Ann. Probab, 28(3), pp.1336~1352 (2000)[DOI]
  10. 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)[DOI]
  11. M. Peligrad, "On the central limit theorem for weakly dependent sequences with a decomposed strong mixing coefficient", Stochastic Process. Appl, 42(2), pp.181~193 (1992)[DOI]
  12. B. L. S. Prakasa Rao, "Conditional independence, conditional mixing and conditional association", Ann. Inst. Statist. Math, 61(2), pp.441~460 (2009)[DOI]
  13. D. Radulovic, "The bootstrap of the mean for strong mixing sequences under minimal conditions", Statist. Probab. Lett, 28(1), pp.65~72 (1996)[DOI]
  14. M. Rosenblatt, "A central limit theorem and a strong mixing condition", Proc. Nat. Acad. Sci. U. S. A, 42(1), pp.43~47 (1956)[DOI]
  15. G. G. Roussas, "On conditional independence, mixing, and association", Stoch. Anal. Appl, 26(6), pp.1274~1309 (2008)[DOI]
  16. A. Sheikhi, "A comprehensive family of copulas to model bivariate random noise and perturbation", Fuzzy Sets Syst, 415, pp.27~36 (2021)[DOI]
  17. M. Sood, "On the minimum node degree and k-connectivity in inhomogeneous random K-out graphs", IEEE Trans. Inf. Theory, 67(10), pp.6868~6893 (2021)[DOI]
  18. X. Wang, "Conditional mean convergence theorems of conditionally dependent random variables under conditions of integrability", Front. Math. China, 10(3), pp.681~696 (2015)[DOI]
  19. R. E. Welsch, "A weak convergence theorem for order statistics from strong-mixing processes", Ann. Math. Statist, 42(5), pp.1637~1646 (1971)[DOI]
  20. S. C. Yang, "Maximal moment inequality for partial sums of strong mixing sequences and application", Acta Math. Sin. (Engl. Ser.), 23(6), pp.1013~1024 (2007)[DOI]
  21. R. Yokoyama, "Moment bounds for stationary mixing sequences", Z. Wahrsch. Verw. Gebiete, 52(1), pp.45~57 (1980)[DOI]
  22. K. Yoshihara, "The Borel-Cantelli lemma for strong mixing sequences of events and their applications to LIL", Kodai Math. J, 2(2), pp.148~157 (1979)[DOI]
  23. D. -M. Yuan, "Conditional limit theorems for conditionally negatively associated random variables", Monatsh. Math, 161(4), pp.449~473 (2010)[DOI]
  24. D.-M. Yuan, "Some conditional results for conditionally strong mixing sequences of random variables", Sci. China Math, 56(4), pp.845~859 (2013)[DOI]
  25. D. -M. Yuan, "Conditional central limit theorems for a sequence of conditional independent random variables", J. Korean Math. Soc, 51(1), pp.1~15 (2014)[DOI]
  26. D. -M. Yuan, "Conditional limit theorems for conditionally linearly negative quadrant dependent random variables", Monatsh. Math, 166(2), pp.281~299 (2012)[DOI]
  27. D.-M. Yuan, "Conditional versions of limit theorems for conditionally associated random variables", J. Math. Anal. Appl, 376(1), pp.282~293 (2011)[DOI]

관련 논문AI추천

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