An exponential inequality for negatively associated random variables

On the Exponential Inequality for Weighted Sums of a Class of Linearly Negative Quadrant Dependent Random Variables

“…Motivated by the paper above, we establish the exponential inequality for weighted sums of uniformly bounded LNQD random variables. The result obtained extends and improves the corresponding ones given by Ko et al [ 13 ] and Jabbari et al [ 7 ]. Furthermore, we give the precise asymptotics with respect to the rate n −1/2 (log⁡ n ) 1/2 .…”

“…(2) Since LNQD sequences are strictly weaker than NA sequences, as mentioned in Section 1 , Theorem 1 extends Theorem 2.1 in Jabbari et al [ 7 ] from strictly stationary negatively associated setting to weighted LNQD case. In addition, by the analysis mentioned above, we know that the strong convergence rate O (1) n −1/2 log⁡ 1/2 n of ∑ i =1 n ( X i − EX i )/ n is much faster than the relevant one O (1) n −1/3 (log⁡ n ) 2/3 Jabbari et al [ 7 ] obtained only for the special case of geometrically decreasing covariances.…”

“…It is well-known that the exponential inequalities for partial sum ∑ i =1 n ( X i − EX i ) play a very important role in various proofs of limit theorems. One can refer to Yang and Wang [ 4 ], T.-S. Kim and H.-C. Kim [ 5 ], Sung [ 6 ], Jabbari et al [ 7 ], Xing et al [ 8 ], Sung [ 9 ], and so on for further comprehension. As for the limit results about LNQD sequence, one can refer to Newman [ 2 ], Zhang [ 10 ], H. Kim and T. Kim [ 11 ], Wang and Zhang [ 12 ], and references therein.…”

On the exponential inequalities for negatively dependent random variables

“…On the other hand, the exponential inequalities for negatively associated random variables were obtained by many authors. We refer to Christofides and Hadjikyriakou [2], Jabbari et al [6] and Roussas [12] for bounded negatively associated random variables and Kim and Kim [8], Nooghabi and Azarnoosh [10], Sung [15], Xing [19], Xing and Yang [21] and Xing et al [24] for identically distributed negatively associated random variables with the finite Laplace transforms. The next dependence notion is negative dependence.…”

On the Almost sure Convergence Rate for Weighted Sums of Negatively Associated Random Variables with Application to Priestley-Chao Estimate

“…Some examples contain: (1) multinomial, (2) convolution of unlike multinomial, (3) multivariate hypergeometric, (4) Dirichlet compound multinomial, (5) negatively correlated normal distribution, (6) permutation distribution, (7) random sampling without replacement and (8) joint distribution of ranks. One can refer to Joag-Dev and Proschan [1], Newman [2], Matula [3], Su et al [4], Yang [5,6] and Jabbari, Jabbari and Azarnoosh [7] for further understanding.…”