The Weak Convergence for Functions of Negatively Associated Random Variables
By Li-Xin Zhang. 2001
47 citations recorded by the source corpus.
Let {Xn, n?1} be a sequence of stationary negatively associated random variables, Sj(l)=?li=1Xj+i, Sn=?ni=1Xi. Suppose that f(x) is a real function. Under some suitable conditions, the central limit theorem and the weak convergence for sums?j=1nfSj(l)l,n?1,are investigated. Applications to limiting distributions of estimators of VarSn are also discussed.
Subfields: Finance, Management Science and Operations Research, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/6cb10c895d28389819dfb8682a52f43be3a565b5
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Citations in the corpus
- Exponential inequalities under the sub-linear expectations with applications to laws of the iterated logarithm (2014, background): “…classical negatively dependent random variables can be found in literature (c.f. Newman (1984), Newman and Wright (1981), Su, Zhao and Wang (1997), Zhang (2001b) etc), it is difficult to establish a central limit theorem for non-independent random variables under the sub- linear expectations.”
- Strong limit theorems for extended independent and extended negatively dependent random variables under non-linear expectations (2016, unknown): “One can refer to Joag-Dev and Proschan (1983), Newman (1984), Matula (1992), Su et al (1997), Shao and Su (1999), Shao (2000), Zhang (2001a, 2001b) etc.”
- Rosenthal’s inequalities for independent and negatively dependent random variables under sub-linear expectations with applications (2014, methodology): “For moment inequalities of partial sums of the classical negatively dependent random variables and related strong limit theorems, one can refer to Shao (2000), Su, Zhao and Wang (1997), Yuan and An (2009), Zhang (2000, 2001a, 2001b), Zhang and Wen (2001) etc.”