TY - GEN
T1 - Asymptotically optimal multistage tests for iid data
AU - Xing, Yiming
AU - Fellouris, Georgios
N1 - This research was supported by the US National Science Foundation under grant ATD-1737962 through the University of Illinois at Urbana-Champaign.
PY - 2022
Y1 - 2022
N2 - The problem of testing two simple hypotheses about the distribution of iid random elements is considered. In particular, the focus is on multistage tests that control the two error probabilities below arbitrary, user-specified levels. A novel multistage test is proposed, analyzed, and shown to achieve the optimal expected sample size under both hypotheses, in the class of all sequential tests with the same error control, to a first-order approximation as the two target error probabilities go to zero at arbitrary rates. The proposed test is compared, both theoretically and numerically, with a multistage test that enjoys the same asymptotic optimality property under one of the two hypotheses, while performing much worse under the other.
AB - The problem of testing two simple hypotheses about the distribution of iid random elements is considered. In particular, the focus is on multistage tests that control the two error probabilities below arbitrary, user-specified levels. A novel multistage test is proposed, analyzed, and shown to achieve the optimal expected sample size under both hypotheses, in the class of all sequential tests with the same error control, to a first-order approximation as the two target error probabilities go to zero at arbitrary rates. The proposed test is compared, both theoretically and numerically, with a multistage test that enjoys the same asymptotic optimality property under one of the two hypotheses, while performing much worse under the other.
KW - 3-stage test
KW - asymptotic optimality
KW - multistage tests
KW - sequential testing
KW - sequential thresholding
UR - http://www.scopus.com/inward/record.url?scp=85133789440&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85133789440&partnerID=8YFLogxK
U2 - 10.1109/ISIT50566.2022.9834797
DO - 10.1109/ISIT50566.2022.9834797
M3 - Conference contribution
AN - SCOPUS:85133789440
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 2985
EP - 2990
BT - 2022 IEEE International Symposium on Information Theory, ISIT 2022
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2022 IEEE International Symposium on Information Theory, ISIT 2022
Y2 - 26 June 2022 through 1 July 2022
ER -