# UNIFORM MODERATE DEVIATION OF SAMPLE QUANTILES AND ORDER STATISTICS

• Xu, ShouFang (Department of Mathematics and Information Science Xinxiang University) ;
• Miao, Yu (College of Mathematics and Information Science Henan Normal University)
• Published : 2014.09.30

#### Abstract

In this article, we establish the $\mathfrak{F}_p$-uniform moderate deviation principles of the sample quantiles and order statistics for a sequence of independent and identically distributed samples.

#### References

1. R. R. Bahadur, A note on quantiles in large samples, Ann. Math. Statist. 37 (1966), no. 3, 577-580. https://doi.org/10.1214/aoms/1177699450
2. H. A. David, Order Statistics, Wiley, New York, 1981.
3. A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications, Springer, New York, 1998.
4. Y. Miao, Y. X. Chen, and S. F. Xu, Asymptotic properties of the deviation between order statistics and p-quantile, Comm. Statist. Theory Methods. 40 (2011), no. 1, 8-14. https://doi.org/10.1080/03610920903350523
5. Y. Miao, S. F. Xu, and A. Peng, Almost sure central limit theorem of sample quantiles, Adv. Decis. Sci. 2012 (2012), Article ID 671942, 7 pages.
6. R. J. Serfling, Approximation Theorems of Mathematical Statistics, John Wiley & Sons, Inc., New York, 1980.
7. S. F. Xu and Y. Miao, Limit behaviors of the deviation between the sample quantiles and the quantile, Filomat. 25 (2011), no. 2, 197-206. https://doi.org/10.2298/FIL1102197X
8. R. Zielinski, Uniform strong consistency of sample quantiles, Statist. Probab. Lett. 37 (1998), no. 2, 115-119. https://doi.org/10.1016/S0167-7152(97)00108-9