On randomized confidence intervals for the binomial probability
Abstract
Suppose that X1,X2,...,Xn are independent and identically Bernoulli(theta) distributed. Also suppose that our aim is to find an exact confidence interval for theta that is the intersection of a 1-α/2 upper confidence interval and a 1-α/2 lower confidence interval. The Clopper-Pearson interval is the standard such confidence interval for theta, which is widely used in practice. We consider the randomized confidence interval of Stevens, 1950 and present some extensions, including pseudorandomized confidence intervals. We also consider the "data-randomized" confidence interval of Korn, 1987 and point out some additional attractive features of this interval. We also contribute to the discussion about the practical use of such confidence intervals.
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