Depth estimators and tests based on the likelihood principle with application to regression

Authors:
Christine H. Müller
Affiliations:
Institute of Mathematics, Carl von Ossietzky University of Oldenburg, Postfach 2503, D-26111 Oldenburg, Germany
Venue:
Journal of Multivariate Analysis
Year:
2005

Citing 4
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Abstract

We investigate depth notions for general models which are derived via the likelihood principle. We show that the so-called likelihood depth for regression in generalized linear models coincides with the regression depth of Rousseeuw and Hubert (J. Amer. Statist. Assoc. 94 (1999) 388) if the dependent observations are appropriately transformed. For deriving tests, the likelihood depth is extended to simplicial likelihood depth. The simplicial likelihood depth is always a U-statistic which is in some cases not degenerated. Since the U-statistic is degenerated in the most cases, we demonstrate that nevertheless the asymptotic distribution of the simplicial likelihood depth and thus asymptotic @a-level tests for general types of hypotheses can be derived. The tests are distribution-free. We work out the method for linear and quadratic regression.