Shape analysis in the light of simplicial depth estimators: 51–54 (original) (raw)

In this paper we present the maximum simplicial depth estimator and compare it to the ordinary least square estimator in examples from 2D shape analysis focusing on bivariate and multivariate allometrical problems from zoology. 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. In applications where outliers in the x- or y-axis direction occur in the data and residuals from ordinary least-square (OLS) linear regression model are not normally distributed, we recommend the use of the maximum simplicial depth estimators. For generalising the median to higher-dimensional settings, a variety of different maximum depth estimators have been introduced. They extend, for example, the halfplane location depth of Tukey. Let Z1,..., ZN be independent and identically distributed bivariate random variables, Zn ∈ Z ⊂ R 2, n = 1, 2,..., N. For given observati...

Sign up for access to the world's latest research.

checkGet notified about relevant papers

checkSave papers to use in your research

checkJoin the discussion with peers

checkTrack your impact