Random Sieves and Generalized Leader-election Procedures
-
Published:2023-08-15
Issue:SI
Volume:52
Page:13-25
-
ISSN:1026-597X
-
Container-title:Austrian Journal of Statistics
-
language:
-
Short-container-title:AJS
Author:
Dong Congzao,Marynych Alexander,Melnykov Viacheslav
Abstract
A random sieve of the set of positive integers N is an infinite sequence of nested subsets N = S0 ⊃ S1 ⊃ S2 ⊃ · · · such that Sk is obtained from Sk−1 by removing elements of Sk−1 with the indices outside Rk and enumerating the remaining elements inthe increasing order. Here R1 , R2 , . . . is a sequence of independent copies of an infinite random set R ⊂ N. We prove general limit theorems for Sn and related functionals, as n → ∞.
Publisher
Austrian Statistical Society
Subject
Applied Mathematics,Statistics, Probability and Uncertainty,Statistics and Probability