Geodesic
Estimates for order statistics in terms of quantiles
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 25, Tome 457 (2017), pp. 265-275

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $X_1,\dots, X_n$ be independent non-negative random variables with cumulative distribution functions $F_1,F_2,\dots,F_n$, each satisfying certain (rather mild) conditions. We show that the median of $k$-th smallest order statistic of the vector $(X_1,\dots,X_n)$ is equivalent to the quantile of order $(k-1/2)/n$ with respect to the averaged distribution $F=\frac1n\sum_{i=1}^n F_i$. 
@article{ZNSL_2017_457_a13,
     author = {A. E. Litvak and K. Tikhomirov},
     title = {Estimates for order statistics in terms of quantiles},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {265--275},
     publisher = {mathdoc},
     volume = {457},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_457_a13/}
}
TY  - JOUR
AU  - A. E. Litvak
AU  - K. Tikhomirov
TI  - Estimates for order statistics in terms of quantiles
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2017
SP  - 265
EP  - 275
VL  - 457
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2017_457_a13/
LA  - en
ID  - ZNSL_2017_457_a13
ER  - 
%0 Journal Article
%A A. E. Litvak
%A K. Tikhomirov
%T Estimates for order statistics in terms of quantiles
%J Zapiski Nauchnykh Seminarov POMI
%D 2017
%P 265-275
%V 457
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2017_457_a13/
%G en
%F ZNSL_2017_457_a13
A. E. Litvak; K. Tikhomirov. Estimates for order statistics in terms of quantiles. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 25, Tome 457 (2017), pp. 265-275. http://geodesic.mathdoc.fr/item/ZNSL_2017_457_a13/