Some inequalities for a LNQD sequence with applications

详细信息    查看全文

• 作者：Yongming Li (1)
  Jianhua Guo (1)
  Naiyi Li (2)
  
• 关键词：LNQD sequence ; characteristic function inequality ; exponential inequality ; moment inequality ; asymptotic normality
• 刊名：Journal of Inequalities and Applications
• 出版年：2012
• 出版时间：December 2012
• 年：2012
• 卷：2012
• 期：1
• 全文大小：182KB
• 参考文献：1. Lehmann EL: Some concepts of dependence. / Ann. Math. Stat. 1966, 37:1137鈥?153. CrossRef
  2. Newman CM: Asymptotic independence and limit theorems for positively and negatively dependent random variables. In / Statistics and Probability. Edited by: Tong YL. Inst. Math. Statist., Hayward; 1984:127鈥?40. [ / 5]
  3. Joag-Dev K, Proschan F: Negative association of random variables with applications. / Ann. Stat. 1983,11(1):286鈥?95. CrossRef
  4. Zhang LX: A functional central limit theorem for asymptotically negatively dependent random fields. / Acta Math. Hung. 2000, 86:237鈥?59. CrossRef
  5. Ko MH, Choi YK, Choi YS: Exponential probability inequality for linearly negative quadrant dependent random variables. / Commun. Korean Math. Soc. 2007, 22:137鈥?43. CrossRef
  6. Ko MH, Ryu DH, Kim TS: Limiting behaviors of weighted sums for linearly negative quadrant dependent random variables. / Taiwan. J. Math. 2007,11(2):511鈥?22.
  7. Wang XJ, Hu SH, Yang WZ, Li XQ: Exponential inequalities and complete convergence for a LNQD sequence. / J. Korean Stat. Soc. 2010, 39:555鈥?64. CrossRef
  8. Wu YF, Guan M: Mean convergence theorems and weak laws of large numbers for weighted sums of dependent random variables. / J. Math. Anal. Appl. 2011, 377:613鈥?23. CrossRef
  9. Roussas GG: Positive and negative dependence with some statistical applications. In / Asymptotics, Nonparametrics, and Time Series. Edited by: Ghosh S, Puri ML. CRC Press, Boca Raton; 1999:757鈥?87.
  10. Roussas GG, Tran LT, Ioannides DA: Fixed design regression for time series: asymptiotic normality. / J. Multivar. Anal. 1992, 40:162鈥?91. CrossRef
  11. Yang SC: Maximal moment inequality for partial sum of strong mixing sequences and application. / Acta Math. Sin. Engl. Ser. 2007,23(6):1013鈥?024. CrossRef
  
• 作者单位：Yongming Li (1)
  Jianhua Guo (1)
  Naiyi Li (2)
  
  1. Department of Mathematics, Shangrao Normal University, Shangrao, 334001, China
  2. Department of Mathematics, Guangdong Ocean University, Zhanjiang, Guangdong, 524088, China
  
• ISSN：1029-242X

文摘

In this paper, some inequalities for a linearly negative quadrant dependent (LNQD) sequence are obtained. As their application, the asymptotic normality of the weight function estimate for a regression function is established, which extends the results of Roussas et al. (J. Multivar. Anal. 40:162-291, 1992) and Yang (Acta. Math. Sin. Engl. Ser. 23(6):1013-1024, 2007) for the strong mixing case to the LNQD case. MSC: 60E15, 62G08, 62E20.