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

Christine H. Müller

Journal of Multivariate Analysis, 2005, vol. 95, issue 1, 153-181

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 [alpha]-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.

Keywords: Likelihood; depth; Simplicial; depth; Regression; depth; Generalized; linear; models; Logistic; regression; Poisson; distribution; Exponential; distribution; Polynomial; regression; Degenerated; U-statistic; Distribution-free; tests; Spectral; decomposition (search for similar items in EconPapers)
Date: 2005
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047-259X(04)00131-9
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:95:y:2005:i:1:p:153-181

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().