Simplical depth estimators and tests in examples from shape analysis

@article{1067013,
   author = {Katina, Stanislav and Wellmann, R. and Muller, Ch.H.},
   article_location = {Bratislava},
   article_number = {1},
   keywords = {simplicial depth; maximum depth estimator; distribution-free tests; one-sample tests; two-sample tests; shape analysis; allometry},
   language = {eng},
   issn = {1210-3195},
   journal = {Tatra Mountains Mathematical Publications},
   title = {Simplical depth estimators and tests in examples from shape analysis},
   url = {http://tatra.mat.savba.sk/},
   volume = {39},
   year = {2008}
}

TY  - JOUR
ID  - 1067013
AU  - Katina, Stanislav - Wellmann, R. - Muller, Ch.H.
PY  - 2008
TI  - Simplical depth estimators and tests in examples from shape analysis
JF  - Tatra Mountains Mathematical Publications
VL  - 39
IS  - 1
SP  - 95-104
EP  - 95-104
PB  - Matematický ústav SAV
SN  - 12103195
KW  - simplicial depth
KW  - maximum depth estimator
KW  - distribution-free tests
KW  - one-sample tests
KW  - two-sample tests
KW  - shape analysis
KW  - allometry
UR  - http://tatra.mat.savba.sk/
N2  - 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, theta = (theta1, theta2)T in R2 and theta = (theta1, theta2, theta3)T in R3, where theta3 = 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.
ER  - 

KATINA, Stanislav, R. WELLMANN a Ch.H. MULLER. Simplical depth estimators and tests in examples from shape analysis. \textit{Tatra Mountains Mathematical Publications}. Bratislava: Matematický ústav SAV, 2008, roč.~39, č.~1, s.~95-104. ISSN~1210-3195.