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Buehler confidence limits and nesting
Author(s) -
Kabaila Paul,
Lloyd Chris J.
Publication year - 2004
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2004.00343.x
Subject(s) - limit (mathematics) , mathematics , nesting (process) , range (aeronautics) , function (biology) , statistic , value (mathematics) , upper and lower bounds , statistics , mathematical analysis , materials science , evolutionary biology , metallurgy , composite material , biology
Summary The Buehler 1 –α upper confidence limit is as small as possible, subject to the constraints that its coverage probability is at least 1 –α and that it is a non‐decreasing function of a pre‐specified statistic T . This confidence limit has important biostatistical and reliability applications. Previous research has examined the way the choice of T affects the efficiency of the Buehler 1 –α upper confidence limit for a given value of α. This paper considers how T should be chosen when the Buehler limit is to be computed for a range of values of α. If T is allowed to depend on α then the Buehler limit is not necessarily a non‐increasing function of α, i.e. the limit is ‘non‐nesting’. Furthermore, non‐nesting occurs in standard and practical examples. Therefore, if the limit is to be computed for a range [α L , α U ]of values of α, this paper suggests that T should be a carefully chosen approximate 1 –α L upper limit for θ. The choice leads to Buehler limits that have high statistical efficiency and are nesting.