Asymptotic Behavior of Sample Mean Direction for Spheres

✍ Scribed by Harrie Hendriks; Zinoviy Landsman; Frits Ruymgaart

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 546 KB
• Volume: 59
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1006/jmva.1996.0057

✦ Synopsis

In this note we consider some asymptotic properties of empirical mean direction on spheres. We do not require any symmetry for the underlying density. Thus our results provide the framework for an asymptotic inference regarding mean direction under very weak model assumptions. Mean direction is a specialization of the more general concept of mean location applicable to arbitrary (compact) submanifolds of Euclidean space, to which the methods of this paper could be applied. 1996 Academic Press, Inc.

1. Introduction

In this paper we derive some asymptotic results for the empirical mean direction on spheres in an intrinsic manner that allow for generalization to more complicated manifolds. Moreover, we do not impose any symmetry condition on the underlying density. Thus our results provide the essential ingredients for estimating, hypothesis testing, and constructing confidence intervals without any symmetry restriction.