Efficient three-stage $t$-tests

Details Efficient three-stage $t$-tests Efficient three-stage $t$-tests

2006-11-22

arxiv.org/abs/math/0611683v1

IMS Lecture Notes--Monograph Series 2006, Vol. 50, 105-111

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/074921706000000626 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/

Scientific paper

10.1214/074921706000000626

Three-stage $t$-tests of separated one-sided hypotheses are derived, extending Lorden's optimal three-stage tests for the one-dimensional exponential family by using Lai and Zhang's generalization of Schwarz's optimal fully-sequential tests to the multiparameter exponential family. The resulting three-stage $t$-tests are shown to be asymptotically optimal, achieving the same average sample size as optimal fully-sequential tests.

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