Timeline for Order statistic - Rate of convergence of a p-quantile to the expectation

11 events

when toggle format	what		by	license	comment
Sep 30, 2020 at 9:09	history	edited	jonasvw	CC BY-SA 4.0	edited body
Nov 26, 2019 at 16:04	vote	accept	jonasvw
Nov 25, 2019 at 16:28	history	edited	Iosif Pinelis		edited tags
Nov 25, 2019 at 16:28	answer	added	Iosif Pinelis		timeline score: 4
Nov 25, 2019 at 15:26	comment	added	jonasvw		Yes, I clarified the notation. Indeen, it boils down to a Beta function and solvable numerically (if I can get my hands on mathematica), I just hoped there is a nice argument here, "proved by mathematica" doesn't sound too nice in a paper :-)
Nov 25, 2019 at 15:24	history	edited	jonasvw	CC BY-SA 4.0	added 68 characters in body
Nov 25, 2019 at 15:14	comment	added	user44143		Once there's an answer to the question from @IosifPinelis, I think this will reduce to a problem about Beta functions where Mathematica will be able to run easy numerical simulations and probably provide a limit.
Nov 25, 2019 at 15:04	comment	added	Iosif Pinelis		What is $\mathbb E_{F_n}[X\|X\leq F_n^{-1}(p)]$? In particular, what is $X$ there? Is $\mathbb E_{F_n}[X\|X\leq F_n^{-1}(p)]$ the conditional expectation of the $q$th largest order statistic (say $Y_q$) given that $Y_q\le F_n^{-1}(p)$?
Nov 25, 2019 at 14:48	history	edited	jonasvw	CC BY-SA 4.0	added 6 characters in body
Nov 25, 2019 at 13:10	review	First posts
Nov 25, 2019 at 13:29
Nov 25, 2019 at 13:07	history	asked	jonasvw	CC BY-SA 4.0