Exponential probability inequalities for WNOD random variables and their applications

Aiting Shen1, Mei Yao2,3, Wenjuan Wang1, Andrei Volodin4
1Anhui University
2Hefei University of Technology
3Shandong University
4University of Regina

Tóm tắt

Từ khóa


Tài liệu tham khảo

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)

Yang, W.Z., Liu, T.T., Wang, X.J., Hu, S.H.: On the Bahadur representation of sample quantiles for widely orthant dependent sequences. Filomat 28(7), 1333–1343 (2014)