Premium
A central limit theorem for sums of correlated products
Author(s) -
Hooghiemstra G.,
Keane M.
Publication year - 1997
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/1467-9574.00035
Subject(s) - mathematics , central limit theorem , integer (computer science) , sequence (biology) , limit (mathematics) , combinatorics , discrete mathematics , law of large numbers , random variable , mathematical analysis , statistics , biology , computer science , genetics , programming language
Consider a sequence of random points placed on the nonnegative integers with i.i.d. geometric (1/2) interpoint spacings y i . Let x i denote the numbers of points placed at integer i . We prove a central limit theorem for the partial sums of the sequence x 0 y 0 , x 1 y 1 , . . . The problem is connected with a question concerning different bootstrap procedures.