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- Title
Reduced-bias Moment Approximations in Original Units When Using Multivariate Box-Cox Transformations.
- Authors
Perry, Marcus B.
- Abstract
Motivated by A-10 single engine aircraft climb experiments, we demonstrate use of the multivariate Box-Cox power transformations in fitting normal-theory linear models to a q-variate response vector Y. As predictions in the original units of the response are often desired, a retransformation of the fitted model back to the original units can be performed. Unfortunately, Jensen's inequality suggests that for a nonlinear transformation, such an approach can induce significant bias into the retransformed values. Further, although the retransformation offers a direct estimate of E( Y), it offers no direct estimates for the variances and covariances of Y. An estimate for the variance-covariance matrix can be useful when constructing approximate joint prediction regions on Y. To address these concerns, we consider the class of multivariate Box-Cox transformations and derive a closed-form approximation to
- Subjects
LINEAR statistical models; MULTIVARIATE analysis; JENSEN'S inequality; AERONAUTICAL charts; ITERATIVE methods (Mathematics); PREDICTION models
- Publication
Quality & Reliability Engineering International, 2017, Vol 33, Issue 2, p297
- ISSN
0748-8017
- Publication type
Article
- DOI
10.1002/qre.2004