Simplical depth estimators and tests in examples from shape analysis

Rok, strany: 2008, 95 - 104

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 antropology. We compare two types of estimators derived under different subsets of parametric space on the basis of the lilnear regression model $θ = (θ₁, θ₂)^T \in \mathbb R²$ and $θ = (θ₁, θ₂, θ₃)^T \in \mathbb R³$, where $θ₃ = 0$. We also discuss monotonically decreasing linear regression models in special situation. In applications where outliers in $x$- or $y$-axis dirrection 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.

ISO 690:

Katina, S., Wellmann, R., Mϋller, C. 2008. Simplical depth estimators and tests in examples from shape analysis. In Tatra Mountains Mathematical Publications, vol. 39, no.1, pp. 95-104. 1210-3195.

APA:

Katina, S., Wellmann, R., Mϋller, C. (2008). Simplical depth estimators and tests in examples from shape analysis. Tatra Mountains Mathematical Publications, 39(1), 95-104. 1210-3195.