Simplified simplicial depth for regression and autoregressive growth processes

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dc.contributor.authorKustosz, Christoph P.
dc.contributor.authorMüller, Christine H.
dc.contributor.authorWendler, Martin
dc.date.accessioned2014-10-09T08:02:42Z
dc.date.available2014-10-09T08:02:42Z
dc.date.issued2014-10-09
dc.description.abstractWe simplify simplicial depth for regression and autoregressive growth processes in two directions. At first we show that often simplicial depth reduces to counting the subsets with alternating signs of the residuals. The second simplification is given by not regarding all subsets of residuals. By consideration of only special subsets of residuals, the asymptotic distributions of the simplified simplicial depth notions are normal distributions so that tests and confidence intervals can be derived easily. We propose two simplifications for the general case and a third simplification for the special case where two parameters are unknown. Additionally, we derive conditions for the consistency of the tests. We show that the simplified depth notions can be used for polynomial regression, for several nonlinear regression models, and for several autoregressive growth processes. We compare the efficiency and robustness of the different simplified versions by a simulation study concerning the Michaelis-Menten model and a nonlinear autoregressive process of order one.en
dc.identifier.urihttp://hdl.handle.net/2003/33641
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-15516
dc.language.isoen
dc.relation.ispartofseriesDiscussion Paper / SFB 823;33/2014
dc.subjectalternating signen
dc.subjectconsistencyen
dc.subjectasymptotic distributionen
dc.subjectrobustnessen
dc.subjectdistribution-free testen
dc.subject.ddc310
dc.subject.ddc330
dc.subject.ddc620
dc.titleSimplified simplicial depth for regression and autoregressive growth processesen
dc.typeTextde
dc.type.publicationtypeworkingPaperde
dcterms.accessRightsopen access

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