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TIGHT UPPER CONFIDENCE LIMITS FROM DISCRETE DATA
Author(s) -
Kabaila Paul,
Lloyd Chris J.
Publication year - 1997
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.1997.tb00535.x
Subject(s) - nuisance parameter , limit (mathematics) , mathematics , upper and lower bounds , scalar (mathematics) , limiting , confidence interval , coverage probability , statistics , distribution (mathematics) , sample size determination , mathematical analysis , geometry , estimator , mechanical engineering , engineering
summary Consider the problem of finding an upper 1 –α confidence limit for a scalar parameter of interest ø in the presence of a nuisance parameter vector θ when the data are discrete. Approximate upper limits T may be found by approximating the relevant unknown finite sample distribution by its limiting distribution. Such approximate upper limits typically have coverage probabilities below, sometimes far below, 1 –α for certain values of (θ, ø). This paper remedies that defect by shifting the possible values t of T so that they are as small as possible subject both to the minimum coverage probability being greater than or equal to 1 –α, and to the shifted values being in the same order as the unshifted t s. The resulting upper limits are called ‘tight’. Under very weak and easily checked regularity conditions, a formula is developed for the tight upper limits.