Bias Reduced Plug-in Estimation in Regression Models for Composite Functions

Abstract

Consider a regression problem in which the objective variable is computed from several intermediate variables by a known deterministic function. This type of setting is used for practical purposes, such as when predicting an indicator that is calculated by a predetermined method from multiple measurements in a factory or plant. In this case, the predicted value of the objective variable can be obtained indirectly by inputting the predicted values of the intermediate variables into the known indicator calculation formula. However, simply substituting the predicted values of the intermediate variables into the indicator formula results in a prediction with a bias derived from noise of the intermediate variables. In this study, we developed a bias-reduced plug-in estimator that considers the effect of noise-derived bias and verified its performance through experiments using artificial data.