KATINA, Stanislav, R. WELLMANN and Ch.H. MULLER. Simplical depth estimators and tests in examples from shape analysis. Tatra Mountains Mathematical Publications. Bratislava: Matematický ústav SAV, 2008, vol. 39, No 1, p. 95-104. ISSN 1210-3195.
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Basic information
Original name Simplical depth estimators and tests in examples from shape analysis
Authors KATINA, Stanislav (703 Slovakia, guarantor, belonging to the institution), R. WELLMANN (276 Germany) and Ch.H. MULLER (276 Germany).
Edition Tatra Mountains Mathematical Publications, Bratislava, Matematický ústav SAV, 2008, 1210-3195.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10103 Statistics and probability
Country of publisher Slovakia
Confidentiality degree is not subject to a state or trade secret
WWW URL
RIV identification code RIV/00216224:14310/08:00061100
Organization unit Faculty of Science
UT WoS 000260473000010
Keywords in English simplicial depth; maximum depth estimator; distribution-free tests; one-sample tests; two-sample tests; shape analysis; allometry
Tags AKR, rivok
Tags International impact, Reviewed
Changed by Changed by: doc. PaedDr. RNDr. Stanislav Katina, Ph.D., učo 111465. Changed: 21. 2. 2013 13:25.
Abstract
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.
Links
CZ.1.07/2.2.00/15.0203, interní kód MUName: Univerzitní výuka matematiky v měnícím se světě (Acronym: Univerzitní výuka matematiky)
Investor: Ministry of Education, Youth and Sports of the CR, 2.2 Higher education
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