When data are transformed to satisfy a spherical normal linear model, the mean θ of a variate in the original scale is a function of the mean μ and variance σ2 of a normal variate. We consider several approximate confidence interval methods for θ, including a new method based on exact confidence intervals for linear functions of μ and σ2. Monte Carlo estimates of coverage probabilities demonstrate the suitability of the new method for applications involving a wide range of data transformations, parameter values and sample sizes.
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Charles E. Land (1974) studied this question.
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