A comparison of two statistical estimators in inverse prediction

Forecasting is primarily concerned with estimating the values of a dependent variable based on new observations of the independent variable. A related and critical issue deals with estimating the values of the independent variable from new observations of the dependent variable. This is termed inverse prediction or statistical calibration and there are two major approaches to it: classical regression and inverse regression. Contrary to the misconception that estimates based on the two methods are invariably similar, it is shown in this paper that they could differ significantly. We seek to identify the factors that contribute to the difference between them and analyse how they interact with each other in simple linear regression models. In addition, based on a comprehensive literature review, we recommend the inverse estimator over the classical estimator except when they are very close to each other.