Robust fitting of a reversible functional linear regression based on trimming

Symmetric regression deals with a reversible functional relation- ship between a set of variables, regardless of the direction of regres- sion. In the case of linear relationships, orthogonal, geometric mean, Pythagorean, and Deming regressions are important examples of sym- metric 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.