A one-sided confidence set hidden under a two-sided sequential test of normal mean.
A one-sided confidence set hidden under a two-sided sequential test of normal mean.
This article demonstrates how to construct a 1 ? ? level confidence set naturally associated a size ? two-sided sequential test of a normal mean ?. If the null hypothesis H0: ? = 0 is rejected by the test, then the confidence set provides a one-sided confidence interval excluding zero for ?. Therefore, based on this confidence set, we can not only reject H0, infer the direction (? > 0 or ? < 0) of ?, but also have the extra information on the magnitude of ? in the direction of inference. The confidence set is clearly more informative than the original test.
one-sided confidence intervals, ordering of observations, two-sided sequential tests
435-438
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a
1999
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a
Liu, Wei
(1999)
A one-sided confidence set hidden under a two-sided sequential test of normal mean.
Statistics and Probability Letters, 41 (4), .
(doi:10.1016/S0167-7152(98)00234-X).
Abstract
This article demonstrates how to construct a 1 ? ? level confidence set naturally associated a size ? two-sided sequential test of a normal mean ?. If the null hypothesis H0: ? = 0 is rejected by the test, then the confidence set provides a one-sided confidence interval excluding zero for ?. Therefore, based on this confidence set, we can not only reject H0, infer the direction (? > 0 or ? < 0) of ?, but also have the extra information on the magnitude of ? in the direction of inference. The confidence set is clearly more informative than the original test.
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Published date: 1999
Keywords:
one-sided confidence intervals, ordering of observations, two-sided sequential tests
Organisations:
Statistics, Mathematical Sciences
Identifiers
Local EPrints ID: 30096
URI: http://eprints.soton.ac.uk/id/eprint/30096
ISSN: 0167-7152
PURE UUID: 086f8ded-8156-405e-ad40-f1dcc2c11a6d
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Date deposited: 14 Mar 2007
Last modified: 16 Mar 2024 02:42
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