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Exponential inequalities and inverse moment for NOD sequence

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Listed:
  • Wang, Xuejun
  • Hu, Shuhe
  • Yang, Wenzhi
  • Ling, Nengxiang

Abstract

Some exponential inequalities for a negatively orthant dependent sequence are obtained. By using the exponential inequalities, we study the asymptotic approximation of inverse moment for negatively orthant dependent random variables, which generalizes and improves the corresponding results of Kaluszka and Okolewski [Kaluszka, M., Okolewski, A., 2004. On Fatou-type lemma for monotone moments of weakly convergent random variables. Statist. Probab. Lett. 66, 45-50], Hu et al. [Hu, S.H., Chen, G.J., Wang, X.J., Chen, E.B., 2007. On inverse moments of nonnegative weakly convergent random variables. Acta Math. Appl. Sin. 30, 361-367(in Chinese)] and Wu et al. [Wu, T.J., Shi, X.P., Miao, B.Q., 2009. Asymptotic approximation of inverse moments of nonnegative random variables. Statist. Probab. Lett. 79, 1366-1371].

Suggested Citation

  • Wang, Xuejun & Hu, Shuhe & Yang, Wenzhi & Ling, Nengxiang, 2010. "Exponential inequalities and inverse moment for NOD sequence," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 452-461, March.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:5-6:p:452-461
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    References listed on IDEAS

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    1. Garcia, Nancy Lopes & Palacios, José Luis, 2001. "On inverse moments of nonnegative random variables," Statistics & Probability Letters, Elsevier, vol. 53(3), pages 235-239, June.
    2. Kaluszka, M. & Okolewski, A., 2004. "On Fatou-type lemma for monotone moments of weakly convergent random variables," Statistics & Probability Letters, Elsevier, vol. 66(1), pages 45-50, January.
    3. Ramsay, Colin M., 1993. "A Note on Random Survivorship Group Benefits," ASTIN Bulletin, Cambridge University Press, vol. 23(1), pages 149-156, May.
    4. Christofides, Tasos C. & Hadjikyriakou, Milto, 2009. "Exponential inequalities for N-demimartingales and negatively associated random variables," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2060-2065, October.
    5. Pittenger, A. O., 1990. "Sharp mean-variance bounds for Jensen-type inequalities," Statistics & Probability Letters, Elsevier, vol. 10(2), pages 91-94, July.
    6. Wu, Tiee-Jian & Shi, Xiaoping & Miao, Baiqi, 2009. "Asymptotic approximation of inverse moments of nonnegative random variables," Statistics & Probability Letters, Elsevier, vol. 79(11), pages 1366-1371, June.
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    Cited by:

    1. Xuejun Wang & Zeyu Si, 2015. "Complete consistency of the estimator of nonparametric regression model under ND sequence," Statistical Papers, Springer, vol. 56(3), pages 585-596, August.
    2. Hongyan Fang & Saisai Ding & Xiaoqin Li & Wenzhi Yang, 2020. "Asymptotic Approximations of Ratio Moments Based on Dependent Sequences," Mathematics, MDPI, vol. 8(3), pages 1-18, March.
    3. Wenzhi Yang & Zhangrui Zhao & Xinghui Wang & Shuhe Hu, 2017. "The large deviation results for the nonlinear regression model with dependent errors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 261-283, June.
    4. Xuejun Wang & Chen Xu & Tien-Chung Hu & Andrei Volodin & Shuhe Hu, 2014. "On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 607-629, September.
    5. Xuejun Wang & Yi Wu & Shuhe Hu & Nengxiang Ling, 2020. "Complete moment convergence for negatively orthant dependent random variables and its applications in statistical models," Statistical Papers, Springer, vol. 61(3), pages 1147-1180, June.
    6. Wenzhi Yang & Haiyun Xu & Ling Chen & Shuhe Hu, 2018. "Complete consistency of estimators for regression models based on extended negatively dependent errors," Statistical Papers, Springer, vol. 59(2), pages 449-465, June.

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