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UNIFORM ASYMPTOTIC EXPANSIONS APPLIED TO SEQUENTIAL t ‐ and t 2 ‐TESTS
Author(s) -
Govindarajulu Z.,
Howard H. C.
Publication year - 1989
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1989.tb00502.x
Subject(s) - mathematics , continuation , asymptotic distribution , normality , sample size determination , calculus (dental) , statistics , estimator , computer science , medicine , dentistry , programming language
summary Using some uniform asymptotic expansions for parabolic cylinder functions recently developed by Olver (1959), various integrals associated with the sequential t‐ and t 2 ‐tests are evaluated asymptotically in terms of the sample size. Then the continuation region inequalities for these tests are inverted and expressed in terms of well known test criteria. It should be pointed out that the inversion of the continuation regions in terms of the well known statistics yields forms for the sequential tests that are more easily applicable by the practitioner than the forms yielded by the method of Rushton. Furthermore, using these inequalities and the asymptotic normality of the test criteria, finite sure termination of sequential t‐ and t 2 ‐test procedures readily follow. Based on simulation studies, power comparisons of the two approximations are also made.