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On the finite sample behavior of testing whether new is better than used of a specified age.

On the finite sample behavior of testing whether new is better than used of a specified age.
On the finite sample behavior of testing whether new is better than used of a specified age.
Hollander, Park and Proschan (1986) proposed a test of new is better than used of a specified age. It is based on large sample normality of the test statistic. There is, however, no study in the literature on its actual size for small and moderate sample sizes. To shed some lights on this, the results of a Monte Carlo simulation study as well as two real data examples are reported and these indicate that the test can have a quite liberal size, especially for small to moderate sample sizes. In order to improve on this weakness, a modified test is proposed and studied. It is noticed that this modified test seems to over-correct the original test to an extent that it becomes unduly conservative sometimes. Hence we propose another modification that combines the original test and the modified test turns out to have its size quite close to the nominal level and is therefore preferable to both the original and modified tests.
asymptotic normality, bias correction, hypotheses test, new better than used of age t0, U-statistics
287-294
Ahmad, Ibrahim A.
84648dd3-2030-4cf4-a397-d89699c75ef1
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a
Zhang, Ying
a1a5b530-992a-41b3-94d8-043590122036
Ahmad, Ibrahim A.
84648dd3-2030-4cf4-a397-d89699c75ef1
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a
Zhang, Ying
a1a5b530-992a-41b3-94d8-043590122036

Ahmad, Ibrahim A., Liu, Wei and Zhang, Ying (2004) On the finite sample behavior of testing whether new is better than used of a specified age. Metrika, 60 (3), 287-294. (doi:10.1007/s001840300311).

Record type: Article

Abstract

Hollander, Park and Proschan (1986) proposed a test of new is better than used of a specified age. It is based on large sample normality of the test statistic. There is, however, no study in the literature on its actual size for small and moderate sample sizes. To shed some lights on this, the results of a Monte Carlo simulation study as well as two real data examples are reported and these indicate that the test can have a quite liberal size, especially for small to moderate sample sizes. In order to improve on this weakness, a modified test is proposed and studied. It is noticed that this modified test seems to over-correct the original test to an extent that it becomes unduly conservative sometimes. Hence we propose another modification that combines the original test and the modified test turns out to have its size quite close to the nominal level and is therefore preferable to both the original and modified tests.

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More information

Published date: 2004
Keywords: asymptotic normality, bias correction, hypotheses test, new better than used of age t0, U-statistics
Organisations: Statistics

Identifiers

Local EPrints ID: 30119
URI: https://eprints.soton.ac.uk/id/eprint/30119
PURE UUID: c955de76-8ae1-4d7a-864e-08f798b24ce0
ORCID for Wei Liu: ORCID iD orcid.org/0000-0002-4719-0345

Catalogue record

Date deposited: 11 May 2006
Last modified: 20 Jul 2019 01:23

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