TY - JOUR
T1 - Convergence of series of moments on general exponential inequality
AU - Lita da Silva, João
AU - Lourenço, Vanda
N1 - info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F04035%2F2020/PT#
info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00297%2F2020/PT#
PY - 2022/2
Y1 - 2022/2
N2 - For an array (Formula presented.) of random variables and a sequence (Formula presented.) of positive numbers, sufficient conditions are given under which, for all (Formula presented.), (Formula presented.) where (Formula presented.) denotes the positive part of x and (Formula presented.), (Formula presented.). Our statements are announced in a general setting allowing to conclude the previous convergence for well-known dependent structures. As an application, we study complete consistency and consistency in the rth mean of cumulative sum type estimators of the change in the mean of dependent observations.
AB - For an array (Formula presented.) of random variables and a sequence (Formula presented.) of positive numbers, sufficient conditions are given under which, for all (Formula presented.), (Formula presented.) where (Formula presented.) denotes the positive part of x and (Formula presented.), (Formula presented.). Our statements are announced in a general setting allowing to conclude the previous convergence for well-known dependent structures. As an application, we study complete consistency and consistency in the rth mean of cumulative sum type estimators of the change in the mean of dependent observations.
KW - convergence of series of moments
KW - CUSUM-type estimators
KW - dependent random variables
KW - Maximum of partial sums
UR - http://www.scopus.com/inward/record.url?scp=85124743478&partnerID=8YFLogxK
U2 - 10.1080/02331888.2022.2038163
DO - 10.1080/02331888.2022.2038163
M3 - Article
AN - SCOPUS:85124743478
SN - 0233-1888
VL - 56
SP - 73
EP - 96
JO - Statistics
JF - Statistics
IS - 1
ER -