- 期刊
ON THE CHARACTERISTIC FUNCTION OF A SUM OF -DEPENDENT RANDOM VARIABLES
摘要
Let S =f_1 +f_2+...+f_n be a sum of l-dependent random variables of zero mean. Let σ^2= E S^2, L=σ^(-3) Σ_(1≤i≤n)E|f_i|^3. There is a universal constant a such that for a |t| L＜ 1, we have |E exp(itSσ^(-1))| ≤(1+a|t|)sup{(a|t|L) ^(-1/4 in L), exp(-t^2/80)} This bound is a very useful tool in proving Berry-Esseen theorems.
延伸閱讀
- 繆紹昌、陳志賢、劉家頤（2011）。On the Variance of Sum of Independent Bernoulli Random Variables and Shannon Entropy。修平學報，(22)，35-43。https://doi.org/10.29548/BGYY.201103.0003
- Wang, X. C., & Rao, M. B. (1985). A NOTE ON CONVERGENCE OF WEIGHTED SUMS OF RANDOM VARIABLES. International Journal of Mathematics and Mathematical Sciences, 1985(), 805-812. https://doi.org/10.1155/S0161171285000898
- Chen, Y., & Qu, Z. (2013). Precise Large Deviations for Random Sums of END Random Variables with Dominated Variation. ISRN Applied Mathematics, (), 229-238. https://doi.org/10.1155/2013/936301
- NEAMMANEE, K. (2003). CAUCHY APPROXIMATION FOR SUMS OF INDEPENDENT RANDOM VARIABLES. International Journal of Mathematics and Mathematical Sciences, 2003(), 1055-1066-076. https://doi.org/10.1155/S0161171203208206
- Chen, K. J., Cheng, T. L., & Wong, Y. (2022). On Some Properties of a Distribution Derived from Finite Exchangeable Random Variables. 中國統計學報, 60(1), 60-68. https://www.airitilibrary.com/Article/Detail?DocID=05296528-202203-202203110007-202203110007-60-68