A Prediction Interval Estimator for the Original Response When Using Box–Cox Transformations

• Autores: Marcus B. Perry, Michael L. Walker
• Localización: Journal of quality technology: A quarterly journal of methods applications and related topics, ISSN 0022-4065, Nº. 3, 47, 2015, págs. 278-297
• Idioma: inglés
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• Resumen

  • Motivated by electron microscopy experiments, the authors of this article develop an approximate prediction interval on the response variable 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 Box-Cox family. The authors derive a closed-form approximation to the kth moment of the original response variable Y, which is then used to estimate the mean and variance of Y, given parameter estimates obtained from fitting the model in the transformed domain. Chebychev's inequality is then used to construct a 100(1−alpha)% prediction-interval estimator on Y. Using Monte Carlo simulation, the authors assess the width performance of their proposed Chebychev prediction interval, relative to that obtained by employing a more common interval-construction approach. General results suggest that, for a given level of expected coverage, the proposed interval estimator will achieve a smaller mean and variance of the interval width estimates, especially as the number of degrees of freedom beyond that required to estimate model terms is small. The method is applied to two experimental data sets, one involving a standard 2k design and the other involving a 2k design with a split-plot error structure.