International Conference on Numerical Analysis and Applied Mathematics (ICNAAM), Rhodes, Greece, 22 - 28 September 2014, vol.1648
Conference Paper / Full Text
Classical Principal Component Regression (CPCR) and Partial Least Squares Regression (PLSR) both fit a linear relationship between two sets of variables. Both of these two methods could be used in case of number of regressors p smaller than number of observations n (pn). The responses are usually low-dimensional whereas the regressors are very numerous compared to the number of observations. They are the most popular regression techniques that they offer a good solution because they first reduce the dimensionality of the design matrix. SIMPLS algorithm is the leading PLSR algorithm because of its speed, efficiency and results are easier to interpret. However, both of the CPCR and SIMPLS yield unreliable results when the data set contains outlying observations. Therefore, Hubert and Vanden Branden (2003) have been proposed the robust versions of these methods: robust PCR (RPCR) and a robust PLSR (RPLSR) method: RSIMPLS. Moreover, Serneels et al. (2005) have been proposed Partial Robust M-Regression (PRM) that it is a partial version of the robust M-regression. The purpose of this study is to compare robust PLSR methods: RSIMPLS, PRM and a robust PCR method: RPCR, and their classical versions in terms of efficiency, goodness-of-fit and predictive power by performing a simulation study.