Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-13T00:49:48.739Z 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: [email protected]
Xuejun Wang
Affiliation:
School of Mathematical Sciences, Anhui University, Hefei 230601, People's Republic of China E-mail: [email protected]
Shuhe Hu
Affiliation:
School of Mathematical Sciences, Anhui University, Hefei 230601, People's Republic of China E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

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
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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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