A unified framework for contrast research of the latent variable multivariate regression methods

Abstract

This paper focuses on contrast research of four latent variable multivariate regression (LVMR) methods, i.e., principal component regression (PCR), partial least square regression (PLSR), canonical correlation regression (CCR) and reduced rank regression (RRR). The performances are evaluated by mean square error (MSE). A unified framework, called weight-framework, is proposed, where each LVMR method as well as the ordinary least square regression (OLSR) can be represented by a specific Weight matrix. Moreover, three theorems are proved delicately. The first one is coefficient theorem which reveals the relations between the coefficients estimated by the four LVMR methods and OLSR; the second one is MSE theorem which contrasts the calibration performances of the different methods; the third one is fault detection rate (FDR) theorem, which tells the different FDR when LVMR is applied for fault detection. Finally, two simulated data sets and one real data set collected from a benchmark system validate the correctness of our theoretical results.