Simplical depth estimators and tests in examples from shape analysis

In this paper we present the maximum simplicial depth estimator and compare it to the ordinary least square estimator in examples from 2D and 3D shape analysis focusing on bivariate and multivariate allometrical problems from zoology and biological anthropology. We compare two types of estimators derived under different subsets of parametric space on the basis of the linear regression model, θ = (θ1, θ2)T ∈ R2 and θ = (θ1, θ2, θ3)T ∈ R3, where θ3 = 0. We also discuss monotonically decreasing linear regression models in special situations. In applications where outliers in x- or y-axis direction occur in the data and residuals from ordinary least-square linear regression model are not normally distributed, we recommend the use of the maximum simplicial depth estimators