Abstract
Suppose that observations are taken from a population with normal distribution N(μ, σ2) where both μ and σ2 are unknown parameters. Our goal is to design a two-sided test of H0: μ = 0 against Ha: μ≠ 0 which has, at least approximately, size α and power β at |μ| = d > 0, where α, β and d are three preassigned constants. The classical solution is Stein's two-stage procedure, which tends to oversampling, however. Three new procedures are proposed and studied in this paper. They all have both size and power very close to the target values α and β and require only a few more observations than the necessary sample size to achieve our goal if σ2 had been completely known.
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Schedule a callMore From: Journal of the Royal Statistical Society: Series D (The Statistician)
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