Robust fitting of a reversible functional linear regression based on trimming

Symmetric regression deals with a reversible functional relationship between a set of variables, regardless of the direction of regression. In the case of linear relationships, orthogonal, geometric mean, Pythagorean, and Deming regressions are important examples of symmetric regression. However, data contamination can have a serious detrimental effect on statistical inference. Therefore, there is a need to develop a methodology aimed at robust fitting in this setting. The proposed technique is built on the idea of impartial trimming, a well known method to handle data inadequacies for linear regression. The inference is based on a subset of the original sample that is obtained after the simultaneous deletion of potentially outlying observations.