Intrinsic means on the circle: uniqueness, locus and asymptotics

T. Hotz () and S. Huckemann ()

Annals of the Institute of Statistical Mathematics, 2015, vol. 67, issue 1, 177-193

Abstract: This paper gives a comprehensive treatment of local uniqueness, asymptotics and numerics for intrinsic sample means on the circle. It turns out that local uniqueness as well as rates of convergence are governed by the distribution near the antipode. If the distribution is locally less than uniform there, we have local uniqueness and asymptotic normality with a square-root rate. With increased proximity to the uniform distribution the rate can be arbitrarily slow, and in the limit, local uniqueness is lost. Further, we give general distributional conditions, e.g., unimodality, that ensure global uniqueness. Along the way, we discover that sample means can occur only at the vertices of a regular polygon which allows to compute intrinsic sample means in linear time from sorted data. This algorithm is finally applied in a simulation study demonstrating the dependence of the convergence rates on the behavior of the density at the antipode. Copyright The Institute of Statistical Mathematics, Tokyo 2015

Keywords: Circular statistics; Directional statistics; Intrinsic mean; Central limit theorem; Asymptotic normality; Convergence rate (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://hdl.handle.net/10.1007/s10463-013-0444-7 (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:aistmt:v:67:y:2015:i:1:p:177-193

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10463/PS2

DOI: 10.1007/s10463-013-0444-7

Access Statistics for this article

Annals of the Institute of Statistical Mathematics is currently edited by Tomoyuki Higuchi

More articles in Annals of the Institute of Statistical Mathematics from Springer, The Institute of Statistical Mathematics
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().