JOURNAL BROWSE
Search
Advanced SearchSearch Tips
CONDITIONAL CENTRAL LIMIT THEOREMS FOR A SEQUENCE OF CONDITIONAL INDEPENDENT RANDOM VARIABLES
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
CONDITIONAL CENTRAL LIMIT THEOREMS FOR A SEQUENCE OF CONDITIONAL INDEPENDENT RANDOM VARIABLES
Yuan, De-Mei; Wei, Li-Ran; Lei, Lan;
  PDF(new window)
 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.
 Keywords
conditional independence;conditional identical distribution;conditional characteristic function;conditional central limit theorem;
 Language
English
 Cited by
1.
SOME RESULTS ON CONDITIONALLY UNIFORMLY STRONG MIXING SEQUENCES OF RANDOM VARIABLES,;;;

대한수학회지, 2014. vol.51. 3, pp.609-633 crossref(new window)
2.
EXTENSIONS OF SEVERAL CLASSICAL RESULTS FOR INDEPENDENT AND IDENTICALLY DISTRIBUTED RANDOM VARIABLES TO CONDITIONAL CASES,;;

대한수학회지, 2015. vol.52. 2, pp.431-445 crossref(new window)
1.
A conditional version of the extended Kolmogorov–Feller weak law of large numbers, Statistics & Probability Letters, 2015, 97, 99  crossref(new windwow)
2.
A Conditional Approach to Panel Data Models with Common Shocks, Econometrics, 2016, 4, 1, 4  crossref(new windwow)
3.
The limit theorem for maximum of partial sums of exchangeable random variables, Statistics & Probability Letters, 2016, 119, 357  crossref(new windwow)
4.
Some results following from conditional characteristic functions, Communications in Statistics - Theory and Methods, 2016, 45, 12, 3706  crossref(new windwow)
 References
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. crossref(new window)

7.
B. L. S. Prakasa Rao, Conditional independence, conditional mixing and conditional association, Ann. Inst. Statist. Math. 61 (2009), no. 2, 441-460. crossref(new window)

8.
G. G. Roussas, On conditional independence, mixing, and association, Stoch. Anal. Appl. 26 (2008), no. 6, 1274-1309. crossref(new window)

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. crossref(new window)

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. crossref(new window)

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. crossref(new window)

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. crossref(new window)