Robust estimation of location and concentration parameters for the von Mises–Fisher distribution

Shogo Kato () and Shinto Eguchi ()

Statistical Papers, 2016, vol. 57, issue 1, 205-234

Abstract: Robust estimation of location and concentration parameters for the von Mises–Fisher distribution is discussed. A key reparametrisation is achieved by expressing the two parameters as one vector on the Euclidean space. With this representation, we first show that maximum likelihood estimator for the von Mises–Fisher distribution is not robust in some situations. Then we propose two families of robust estimators which can be derived as minimisers of two density power divergences. The presented families enable us to estimate both location and concentration parameters simultaneously. Some properties of the estimators are explored. Simple iterative algorithms are suggested to find the estimates numerically. It is shown that the presented approaches can be utilised to estimate either the location or concentration parameter. A comparison with the existing robust estimators is given as well as discussion on difference and similarity between the two proposed estimators. A simulation study is made to evaluate finite sample performance of the estimators. We apply the proposed methods to a sea star dataset and discuss the selection of the tuning parameters and outlier detection. Copyright Springer-Verlag Berlin Heidelberg 2016

Keywords: Directional data; Divergence; Influence function; Outlier detection; Robust inference; 62H11; 62F35; 62E15 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://hdl.handle.net/10.1007/s00362-014-0648-9 (text/html)
Access to full text is restricted to subscribers.

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:spr:stpapr:v:57:y:2016:i:1:p:205-234

Ordering information: This journal article can be ordered from
http://www.springer. ... business/journal/362

DOI: 10.1007/s00362-014-0648-9

Access Statistics for this article

Statistical Papers is currently edited by C. Müller, W. Krämer and W.G. Müller

More articles in Statistical Papers from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().