Inverse Matrix Problem in Regression for High-Dimensional Data Sets

Forhigh-dimensional chemometric data, the inverse matrix X t X − 1 problem in regression models is a difficulty. Multicollinearity and identification result from the inverse matrix problem. The usage of the least absolute shrinkage and selection operator (LASSO) and partial least squares are two existing ways of dealing with the inverse matrix problem (PLS). For regressing the chemometric data sets, we used extended inverse and beta cube regression. The existing and proposed methods are compared over near-infrared spectra of biscuit dough and Raman spectra analysis of contents of polyunsaturated fatty acids (PUFA). For reliable estimation, Monte Carlo cross-validation has been used. The proposed methods outperform based on the root mean square error, indicating that cube regression and inverse regression are reliable and can be used for diverse high-dimensional data sets.