Approximations to inverse moments of double-indexed weighted SUMS

作者：Yang, Wenzhi; Shi, Xiaoping; Li, Xiaoqin; Hu, Shuhe^*

来源：Journal of Mathematical Analysis and Applications, 2016, 440(2): 833-852.

DOI：10.1016/j.jmaa.2016.03.050

• Inverse moments
• Convergence rate
• Triangular array

In this paper, we investigate some approximations to inverse moments of double indexed weighted sums of random variables. Let {Z(n)} be a sequence of nonnegative independent random -variables and {wni} be a triangular array of nonnegative non-random weights. With the finite first moment, we establish that E(a + Sigma(n)(i=1) w(ni)Z(i) similar to)(-alpha) - (a + Sigma(n)(i=1) (a + Sigma(n)(i=1) wni EZ(i))(-alpha) holds for all a > 0 and alpha > 0. By the finite r-th moment (r > 2), the convergence rate of approximation between E(a + Sigma(n)(i=1) wni EZ(i))(-alpha) a and (a+ Sigma(n)(i=1) w(ni)EZ(i))(-alpha) a > 0 is presented. On the other hand, we obtain some approximations for the estimators of E(Sigma(n)(i=1)w(ni)Z(i)/a + Sigma(n)(i=1)), E(Sigma(n)(i=1)w(ni)Z(i))/a+Sigma(n)(i=1) Z(i))(2) and Var(Sigma(n)(i=1)w(ni)Z(i))/a+Sigma(n)(i=1) Z(i)) for all a > 0. Finally, some examples and simulations are illustrated.

• 出版日期2016-8-15
• 单位安徽大学