Prediction Techniques for Box–Cox Regression Models
回顾了Box-Cox变换回归模型中点预测和区间预测的几种技术，包括插件法、均方误差分析、预测似然和随机模拟，并通过蒙特卡洛研究评估了它们在小样本下的准确性。
Abstract This article reviews several techniques useful for forming point and interval predictions in regression models with Box-Cox transformed variables. The techniques reviewed—plug-in, mean squared error analysis, predictive likelihood, and stochastic simulation—take account of nonnormality and parameter uncertainty in varying degrees. A Monte Carlo study examining their small-sample accuracy indicates that uncertainty about the Box–Cox transformation parameter may be relatively unimportant. For certain parameters, deterministic point predictions are biased, and plug-in prediction intervals are also biased. Stochastic simulation, as usually carried out, leads to badly biased predictions. A modification of the usual approach renders stochastic simulation predictions largely unbiased. KEY WORDS: Mean squared errorPrediction biasPrediction intervalPredictive likelihoodStochastic simulationTransformation