Date Log
NORMAL APPROXIMATION FOR UNORDERED MARTINGALE DIFFERENCE SEQUENCES
Corresponding Author(s) : Le Van Dung
UED Journal of Social Sciences, Humanities and Education,
Vol. 5 No. 1 (2015): UED JOURNAL OF SOCIAL SCIENCES, HUMANITIES AND EDUCATION
Abstract
Of all the limit theorems of the probability theory, the central limit theorem plays an important role in statistical analysis and its application. However, statistical problems cannnot be solved with infinitely large sample sizes, so the problem of “normal approximation” helps to estimate the required sample size to apply central limit theorems. In 1970, Charler Stein introduced his startling technique for normal approximation which is now known as Stein's method. This paper establishes some results of normal approximation for sequences of unordered martingale difference random variables. The results are the extension of those of the independent random variables sequences.
Keywords
Download Citation
Endnote/Zotero/Mendeley (RIS)BibTeX
-
[1] Berry A.C. (1941), “The accuracy of the Gaussian approximation to the sum of independent variates”, Trans. Amer. Math., 49, 122–136.
[2] Choi K. P. and Klass M. J. (1997), “Some best possible prophet inequalities for convex functions of sums of independent variates and unordered martingale difference sequences”, The Annals of Probability, 25, 2, 803–811.
[3] Chen H.Y.L, Goldstein L. and Qi-Man Shao (2011), “Normal approximation by Stein’s method”, Springer Press.
[4] Esseen C. G. (1942), “On the Liapunov limit of error in the theory of probability”, Ark. Mat. Astr. Fys., 28A, 1–19.