Robust tests for one or more allometric lines

In allometry, the study of how size variables scale against each other, it is often of interest to fit lines to bivariate data and test hypotheses about slope and elevation about one or several lines. The nature of the problem suggests that bivariate techniques related to principal component analysis are more appropriate than linear regression. Inference methods have been developed for this problem and are in widespread use, however, we demonstrate that such methods are not robust to bivariate contamination, and propose alternative approaches which are. The new approaches use Huber's M-estimator via a plug-in approach, where robust test procedures have the same form as classical ones, but where we plug in robust estimators of parameters and standard errors in place of classical estimators. Simulations demonstrate that these new procedures are robust against bivariate contamination, and can make accurate inferences even from small samples.