Two-Stage Procedures for Estimating the Difference of Means when the Sampling Cost is Different |
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| Authors: | Makoto Aoshima Nitis Mukhopadhyay Yuko Kobayashi |
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| Affiliation: | 1. Institute of Mathematics , University of Tsukuba , Ibaraki, Japan aoshima@math.tsukuba.ac.jp;3. Department of Statistics , University of Connecticut , Storrs, Connecticut, USA;4. Graduate School of Pure and Applied Sciences , University of Tsukuba , Ibaraki, Japan |
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| Abstract: | Abstract We suppose that there are two independent normal populations, π1: N(μ1, σ2) and π2: N(μ2, a 2σ2), where μ1, μ2, σ2 are unknown but a (0 < a ≤ 1) is known. We suppose that the sampling cost from π2 is more expensive than that from π1. We consider estimating Δ = μ1 ? μ2 by some appropriately constructed fixed-width confidence interval. We give two types of two-stage procedures denoted by 𝒫5 and 𝒫6 for this purpose. Assuming that both two-stage sampling strategies are implementable in some situation, we show that 𝒫6 compares favorably with 𝒫5 and suggest implementing 𝒫6 in practice. We also reaffirm these sentiments with illustrations using a real data set from Mukhopadhyay et al. (2004 Mukhopadhyay , N. , Son , M. S. , and Ko , Y. C. ( 2004 ). A New Two-Stage Sampling Design for Estimating the Maximum Average Time to Flower , Journal of Agricultural, Biological, and Environmental Statistics 9 : 479 – 499 .[Crossref], [Web of Science ®] , [Google Scholar]). |
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| Keywords: | Behrens-Fisher problem Fixed-width confidence interval Sampling cost |
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