Stability of Order Statistics under Dependence
โ Scribed by Tomasz Rychlik
- Book ID
- 110330484
- Publisher
- Springer Japan
- Year
- 2001
- Tongue
- English
- Weight
- 968 KB
- Volume
- 53
- Category
- Article
- ISSN
- 0020-3157
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
If X 1 , ..., X n are random variables we denote by X (1) X (2) ... X (n) their respective order statistics. In the case where the random variables are independent and identically distributed, one may demonstrate very strong notions of dependence between any two order statistics X (i) and X ( j) . I
For r >/1, let Mnr be the rth largest of {X1,... ,X,}, where XI,X2 .... are i.i.d, random variables with common distribution function F such that F(x)< 1 for all x. Define #(x) =F 1(1 -x -~), x>~ 1. {M,r,n>~r} is called regularly stable if Mnr/12(n)--~ 1 in probability and (\*)#(n t)/#(n) ~ h(t)< ve