Landweber Banach Regression in Statistical Learning

In statistical learning, regularization is recommended for handling large models in order to prevent overfitting. The present study aims to investigate the application of an iterative regularization method, based on Landweber iterations in Banach spaces, in high dimensional statistical models. Regularization in Banach spaces is applied to reconstruct solutions which present discontinuities or have a low degree of smoothness. When in statistical models the design matrix is supersaturated, which appears frequently in a majority of industrial applications and experiments, the main scope concerns the indentification of the appropriate active factors and possible interactions as well. Landweber regression will be here tested for variable selection. Several real data sets are analyzed and useful remarks and comparisons concerning the selection of the most apropriate factors are presented.