Depth notions for orthogonal regression

作者：Wellmann Robin^*; Mueller Christine H

来源：Journal of Multivariate Analysis, 2010, 101(10): 2358-2371.

DOI：10.1016/j.jmva.2010.06.008

• Orthogonal regression
• Tangent depth
• Global depth
• Simplicial depth
• Asymptotic tests

Global depth, tangent depth and simplicial depths for classical and orthogonal regression are compared in examples, and properties that are useful for calculations are derived. The robustness of the maximum simplicial depth estimates is shown in examples. Algorithms for the calculation of depths for orthogonal regression are proposed, and tests for multiple regression are transferred to orthogonal regression. These tests are distribution free in the case of bivariate observations. For a particular test problem, the powers of tests that are based on simplicial depth and tangent depth are compared by simulations.

• 出版日期2010-11