Multivariate Prediction in the Original Units When Using Manly's Exponential Transformation

• Activity Number: 140
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Quality and Productivity Section
• Author(s): Michael Walker* and Marcus Perry
• Companies: The University of Alabama and The University of Alabama
• Keywords: data transformations ; linear models ; prediction regions ; transformation bias ; multivariate response

Abstract

Motivated by A-10 single-engine aircraft climb experiments, we develop an approximate prediction ellipsoid on the q-variate response vector Y, where it is assumed that a normal-theory linear model is fit using a transformed version of Y, and the transformation type is contained in the Manly exponential family. We derive closed-form moment approximations in order to estimate the mean and variance of each original response variable, as well as the covariances between the individual responses, given parameter estimates obtained from fitting the model in the transformed domain. Exploiting two multivariate analogs of Chebyshev's inequality we construct a prediction spheroid and ellipsoid, respectively, on the original response vector Y. Using Monte Carlo simulation, we assess the performance of the proposed estimators for the means, variances, and covariances, as well as the coverage performance of the two prediction regions constructed using the proposed estimators.