Exponential probability inequalities for WNOD random variables and their applications
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Asadian, N., Fakoor, V., Bozorgnia, A.: Rosenthal’s type inequalities for negatively orthant dependent random variables. JIRSS 5(1–2), 69–75 (2006)
Chen, P.Y., Hu, T.C., Liu, X., Volodin, A.: On complete convergence for arrays of row-wise negatively associated random variables. Theory Probab. Appl. 52(2), 323–328 (2008)
Chen, Y., Chen, A., Ng, K.W.: The strong law of large numbers for extend negatively dependent random variables. J. Appl. Probab. 47, 908–922 (2010)
Chen, Y., Wang, L., Wang, Y.B.: Uniform asymptotics for the finite-time ruin probabilities of two kinds of nonstandard bidimensional risk models. J. Math. Anal. Appl. 401, 114–129 (2013)
Chow, Y.S.: On the rate of moment convergence of sample sums and extremes. Bull. Inst. Math. Acad. Sin. 16, 177–201 (1988)
Fakoor, V., Azarnoosh, H.A.: Probability inequalities for sums of negatively dependent random variables. Pak. J. Stat. 21, 257–264 (2005)
Hu, T.Z.: Negatively superadditive dependence of random variables with applications. Chin. J. Appl. Probab. Stat. 16, 133–144 (2000)
Li, X.Q., Yang, W.Z., Hu, S.H., Wang, X.J.: The Bahadur representation for sample quantile under NOD sequence. J. Nonparametr. Stat. 23(1), 59–65 (2011)
Liu, L.: Precise large deviations for dependent random variables with heavy tails. Stat. Probab. Lett. 79(9), 1290–1298 (2009)
Liu, X.J., Gao, Q.W., Wang, Y.B.: A note on a dependent risk model with constant interest rate. Stat. Probab. Lett. 82, 707–712 (2012)
Nili Sani, H.R., Amini, M., Bozorgnia, A.: Strong laws for weighted sums of negative dependent random variables. Islam. Repub. Iran J. Sci. 16(3), 261–266 (2005)
Qiu, D.H., Chen, P.Y.: Complete and complete moment convergence for weighted sums of widely orthant dependent random variables. Acta Math. Sin. Engl. Ser. 30(9), 1539–1548 (2014)
Qiu, D.H., Chen, P.Y., Antonini, R.G., Volodin, A.: On the complete convergence for arrays of rowwise extended negatively dependent random variables. J. Korean Math. Soc. 50(2), 379–392 (2013)
Qiu, D.H., Hu, T.C.: Strong limit theorems for weighted sums of widely orthant dependent random variables. J. Math. Res. Appl. 34(1), 105–113 (2014)
Shao, Q.M.: A comparison theorem on moment inequalities between negatively associated and independent random variables. J. Theor. Probab. 13(2), 343–356 (2000)
Shen, A.T.: Some strong limit theorems for arrays of rowwise negatively orthant-dependent random variables. J. Inequal. Appl. 2011, Article ID 93, 10 (2011)
Shen, A.T.: Probability inequalities for END sequence and their applications. J. Inequal. Appl. 2011, Article ID 98, 12 (2011)
Shen, A.T.: On strong convergence for weighted sums of a class of random variables. Abstr. Appl. Anal. 2013, Article ID 216236, 7 (2013)
Shen, A.T.: Bernstein-type inequality for widely dependent sequence and its application to nonparametric regression models. Abstr. Appl. Anal. 2013, Article ID 862602, 9 (2013)
Shen, A.T.: On the strong convergence rate for weighted sums of arrays of rowwise negatively orthant dependent random variables. Revista de la Real Academia de Ciencias Exactas Fisicas y Naturales. Serie A. Matematicas 107, 257–271 (2013)
Sung, S.H.: A note on the complete convergence for arrays of dependent random variables. J. Inequal. Appl. 2011, Article ID 76, 8 (2011)
Sung, S.H.: Complete $$q$$ q moment convergence for arrays of random variables. J. Inequal. Appl. 2013, Article ID 24, 11 (2013)
Wang, K.Y., Wang, Y.B., Gao, Q.W.: Uniform asymptotics for the finite-time ruin probability of a new dependent risk model with a constant interest rate. Methodol. Comput. Appl. Probab. 15(1), 109–124 (2013)
Wang, S.J., Wang, X.J.: Precise large deviations for random sums of END real-valued random variables with consistent variation. J. Math. Anal. Appl. 402, 660–667 (2013)
Wang, X.J., Hu, S.H.: Complete convergence and complete moment convergence for martingale difference sequence. Acta Math. Sin. Engl. Ser. 30(1), 119–132 (2014)
Wang, X.J., Hu, S.H., Yang, W.Z., Ling, N.X.: Exponential inequalities and inverse moment for NOD sequence. Stat. Probab. Lett. 80(5–6), 452–461 (2010)
Wang, X.J., Hu, S.H., Yang, W.Z.: Complete convergence for arrays of rowwise negatively orthant dependent random variables. RACSAM 106(2), 235–245 (2012)
Wang, X.J., Wang, S.J., Hu, S.H., Ling, J.M., Wei, Y.F.: On complete convergence of weighted sums for arrays of rowwise extended negatively dependent random variables. Stochastics: Int. J. Probab. Stoch. Process. 85(6), 1060–1072 (2013)
Wang, X.J., Hu, T.C., Volodin, A., Hu, S.H.: Complete convergence for weighted sums and arrays of rowwise extended negatively dependent random variables. Commun. Stat. Theory Methods 42, 2391–2401 (2013)
Wang, X.J., Deng, X., Zheng, L.L., Hu, S.H.: Complete convergence for arrays of rowwise negatively superadditive-dependent random variables and its applications. Statistics: J. Theor. Appl. Stat. 48(4), 834–850 (2014)
Wang, X.J., Xu, C., Hu, T.C., Volodin, A., Hu, S.H.: On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models. TEST 23, 607–629 (2014)
Wang, X.J., Zheng, L.L., Xu, C., Hu, S.H.: Complete consistency for the estimator of nonparametric regression models based on extended negatively dependent errors. Statistics: J. Theor. Appl. Stat. 49(2), 396–407 (2015)
Wang, Y.B., Li, Y.W., Gao, Q.W.: On the exponential inequality for acceptable random variables. J. Inequal. Appl. 2011, Article ID 40, 1–10 (2011)
Wang, Y.B., Cheng, D.Y.: Basic renewal theorems for a random walk with widely dependent increments and their applications. J. Math. Anal. Appl. 384, 597–606 (2011)
Wang, Y.B., Cui, Z., Wang, K.Y., Ma, X.: Uniform asymptotics of the finite-time ruin probability for all times. J. Math. Anal. Appl. 390, 208–223 (2012)
Wu, Q.Y.: Probability Limit Theory for Mixing Sequences. Science Press of China, Beijing (2006)
Wu, Q.Y.: A strong limit theorem for weighted sums of sequences of negatively dependent random variables. J. Inequal. Appl. 2010, Article ID 383805, 1–8 (2010)
Wu, Q.Y.: A complete convergence theorem for weighted sums of arrays of rowwise negatively dependent random variables. J. Inequal. Appl. 2012, Article ID 50, 1–10 (2012)
Wu, Q.Y., Jiang, Y.Y.: The strong consistency of $$M$$ M estimator in a linear model for negatively dependent random samples. Commun. Stat. Theory Methods 40, 467–491 (2011)
Wu, Y.F., Cabrera, M.O., Volodin, A.: On limiting behavior for arrays of rowwise negatively orthant dependent random variables. J. Korean Stat. Soc. 42, 61–70 (2013)
Wu, Y.F., Zhu, D.J.: Convergence properties of partial sums for arrays of rowwise negatively orthant dependent random variables. J. Korean Stat. Soc. 39(2), 189–197 (2010)
Yang, W.Z., Hu, S.H., Wang, X.J.: Complete convergence for moving average process of martingale differences. Discret. Dyn. Nat. Soc. 2012, Article ID 128492, 1–16 (2012)