Calculation of simplicial depth estimators for polynomial regression with applications
| Authors | |
|---|---|
| Year of publication | 2007 |
| Type | Article in Periodical |
| Magazine / Source | Computational Statistics & Data Analysis |
| MU Faculty or unit | |
| Citation | |
| Web | http://www.sciencedirect.com/science/article/pii/S0167947306003847 |
| Doi | http://dx.doi.org/10.1016/j.csda.2006.10.015 |
| Field | General mathematics |
| Keywords | Polynomial regression; Simplicial depth; Maximum depth estimator; Distribution free tests; One-sample tests; Two-sample tests; Shape analysis |
| Description | A fast algorithm for calculating the simplicial depth of a single parameter vector of a polynomial regression model is derived. Additionally, an algorithm for calculating the parameter vectors with maximum simplicial depth within an affine subspace of the parameter space or a polyhedron is presented. Since the maximum simplicial depth estimator is not unique, l1 and l2 methods are used to make the estimator unique. This estimator is compared with other estimators in examples of linear and quadratic regression. Furthermore, it is shown how the maximum simplicial depth can be used to derive distribution-free asymptotic alpha-level tests for testing hypotheses in polynomial regression models. The tests are applied on a problem of shape analysis where it is tested how the relative head length of the fish species Lepomis gibbosus depends on the size of these fishes. It is also tested whether the dependency can be described by the same polynomial regression function within different populations. |
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