Hostname: page-component-7b7567c8c-7pwfn Total loading time: 0 Render date: 2026-11-12T10:19:57.934Z Has data issue: false hasContentIssue false
  • English
  • Français

MODERATE DEVIATION PRINCIPLE OF SAMPLE QUANTILES AND ORDER STATISTICS

Published online by Cambridge University Press:  23 November 2017

Yi Wu,
Xuejun Wang and
Shuhe Hu
Yi Wu
Affiliation:
School of Mathematical Sciences, Anhui University, Hefei 230601, People's Republic of China E-mail: wxjahdx@126.com
Xuejun Wang
Affiliation:
School of Mathematical Sciences, Anhui University, Hefei 230601, People's Republic of China E-mail: wxjahdx@126.com
Shuhe Hu
Affiliation:
School of Mathematical Sciences, Anhui University, Hefei 230601, People's Republic of China E-mail: wxjahdx@126.com
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

In this paper, we mainly study the moderate deviation principle of sample quantiles and order statistics for stationary m-dependent random variables. The results obtained in this paper extend the corresponding ones for an independent and identically distributed sequence to a stationary m-dependent sequence.

Keywords

moderate deviationorder statisticsp-quantilesample quantilesstationary m-dependent random variables

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 32 , Issue 4 , October 2018, pp. 603 - 614
Copyright
Copyright © Cambridge University Press 2017 

References

1.Adler, A. (2002). Limit theorems for arrays of maximal order statistics. Probability and Mathematical Statistics 22: 211–220.Google Scholar
2.Adler, A. (2004). Complete convergence for arrays of minimal order statistics. International Journal of Mathematics and Mathematical Sciences 44: 2325–2329.Google Scholar
3.Babu, G.J. & Singh, K. (1978). On deviations between empirical and quantile processes for mixing random variables. Journal of Multivariate Analysis 8: 532–549.Google Scholar
4.Bahadur, R.R. (1966). A note on quantiles in large samples. The Annals of Mathematical Statistics 37: 577–580.Google Scholar
5.Childs, A., Balakrishnan, N. & Moshref, M. (2001). Order statistics from non-identical right-truncated Lomax random variables with applications. Statistical Papers 42(2): 187–206.Google Scholar
6.David, H.A. (1981). Order statistics. New York: Wiley.Google Scholar
7.Dembo, A. & Zeitouni, O. (1998). Large deviations techniques and applications. 2nd ed. New York: Springer.Google Scholar
8.Hoeffding, W. & Robbins, H. (1948). The central limit theorem for dependent random variables. Duke Mathematical Journal 15: 773–780.Google Scholar
9.Li, X.Q., Yang, W.Z., Hu, S.H. & Wang, X.J. (2011). The Bahadur representation for sample quantile under NOD sequence. Journal of Nonparametric Statistics 23: 59–65.Google Scholar
10.Ling, N.X. (2008). The Bahadur representation for sample quantiles under negatively associated sequence. Statistics and Probability Letters 78: 2660–2663.Google Scholar
11.Liu, T.T., Zhang, Z.M., Hu, S.H. & Yang, W.Z. (2014). The Berry-Esséen bound of sample quantiles for NA sequence. Journal of Inequalities and Applications 2014, Article ID 79, 7 pages.Google Scholar
12.Miao, Y., Chen, Y.X. & Xu, S.F. (2011). Asymptotic properties of the deviation between order statistics and p-quantile. Communications in Statistics-Theory and Methods 40: 8–14.Google Scholar
13.Park, S. (1996). Fisher information in order statistics. Journal of the American Statistical Association 91: 385–390.Google Scholar
14.Park, S. (2003). On the asymptotic Fisher information in order statistics. Metrika 57: 71–80.Google Scholar
15.Romano, J.P. & Wolf, M. (2000). A more general central limit theorem for m-dependent random variables with unbounded m. Statistics and Probability Letters 47: 115–124.Google Scholar
16.Schönfeld, , (1971). A useful central limit theorem for m-dependent variables. Metrika 17: 116–128.Google Scholar
17.Sen, P.L. (1968). Asymptotic normality of sample quantiles for m-dependent processes. The Annals of Mathematical Statistics 39: 1724–1730.Google Scholar
18.Sen, P.K. (1972). On Bahadur representation of sample quantiles for sequences of φ-mixing random variables. Journal of Multivariate Analysis 2: 77–95.Google Scholar
19.Serfling, R.J. (1980). Approximation theorems of mathematical statistics. New York, Wiley.Google Scholar
20.Xing, G.D. & Yang, S.C. (2011). A remark on the Bahadur representation of sample quantiles for negatively associated sequences. Journal of the Korean Statistical Society 40: 277–280.Google Scholar
21.Xing, G.D., Yang, S.C., Liu, Y. & Yu, K.M. (2012). A note on the Bahadur representation of sample quantiles for α-mixing random variables. Monatshefte für Mathematik 165: 579–596.Google Scholar
22.Xu, S.F. & Miao, Y. (2011). Limit behaviors of the deviation between the sample quantiles and the quantile. Filomat 25: 197–206.Google Scholar
23.Wang, X.J., Hu, S.H. & Yang, W.Z. (2011). The Bahadur representation for sample quantiles under strongly mixing sequence. Journal of Statistical Planning and Inference 141: 655–662.Google Scholar
24.Wang, Y.S., Zhuang, W.W. & Hu, T.Z. (2010). Conditionally stochastic domination of generalized order statistics from two samples. Statistical Papers 51(2): 369–373.Google Scholar
25.Wendler, M. (2011). Bahadur representation for U-quantiles of dependent data. Journal of Multivariate Analysis 102(6): 1064–1079.Google Scholar
26.Yang, W.Z., Wang, X.J., Li, X.Q. & Hu, S.H. (2012). Berry-Esséen bound of sample quantiles for φ-mixing random variables. Journal of Mathematical Analysis and Applications 388: 451–462.Google Scholar
27.Yang, W.Z., Hu, S.H., Wang, X.J. & Ling, N.X. (2012). The Berry-Esséen type bound of sample quantiles for strong mixing sequence. Journal of Statistical Planning and Inference 142: 660–672.Google Scholar
28.Yang, W.Z., Liu, T.T., Wang, X.J. & Hu, S.H. (2014). On the Bahadur representation of sample quantiles for widely orthant dependent sequences. Filomat 28(7): 1333–1343.Google Scholar