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Abstract:
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For confidence interval (CI) problems, researchers generally attempt to minimize the length of the interval, maintaining the coverage probability. By extending this approach to multiple CIs, the optimal Size Investing Strategy is investigated given the global coverage probability 1-q (equivalently global size q) under FWER. To do this, a loss function approach for CI is adopted. The optimal size investing strategy for multiple CIs suggests to match the smaller confidence coefficients for larger standard errors to compensate the effect of the standard errors on the total length. This is different from the optimal size investing strategy for multiple testings (Pena et al., 2011&2015) because the trade-off relation between coverage probability and interval length in Multiple CIs is different from the relation between size and power in multiple testings. Result shows about 5% of the total length decrease compared to the total length by Sidak procedure on the 1,000 location parameters of normal random variables.
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