Prediction intervals for the original response when using Manly’s exponential transformations

Abstract

ABSTRACTMotivated by A-10 single engine aircraft climb experiments, in this article we consider prediction interval estimation in the original units of observation after fitting a linear model using Manly’s exponential transformations. We assume that the residuals obtained from fitting the model in the transformed space are iid zero-mean normal random variables, at least approximately. We discuss the bias in the retransformed mean and derive a reduced bias estimator for the kth moment of the original response, given settings of the design variables. This is then used to compute reduced-bias estimates for the mean and variance of the untransformed response at various locations in design space. We then exploit Chebychev’s inequality, along with our proposed moment estimator, to construct an approximate 100(1 − α)% prediction interval on the original response, given settings of the design factors. We used Monte Carlo simulation to evaluate the performance of our proposed prediction interval estimator relative to a more commonly used alternative in practice. Our results suggest the proposed method is often the better alternative when the sample size is small and/or when the underlying model is misspecified.