Valid confidence intervals for μ, σ when there is only one observation available

02/07/2022

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by   Stephen Portnoy, et al.

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Portnoy (2019) considered the problem of constructing an optimal confidence interval for the mean based on a single observation X ∼N(μ , σ^2). Here we extend this result to obtaining 1-sample confidence intervals for σ and to cases of symmetric unimodal distributions and of distributions with compact support. Finally, we extend the multivariate result in Portnoy (2019) to allow a sample of size m from a multivariate normal distribution where m may be less than the dimension.