Nonparametric comparison of mean directions or mean axes
type: Item
instance of: scholarly article
title: Nonparametric comparison of mean directions or mean axes
zbMATH Open document ID: 0934.62057
author: Rudolf Beran
author: N. I. Fisher
published in: The Annals of Statistics
publication date: 1999-11-09T00:00:00Z
review text: Geological data often contains directions or axes measured in three dimensions. Examples are directions of remanent magnetization of lava cores, axes normal to geological folding planes, or positions on the surface of the earth. Biological measurements may include directions or axes in two dimensions. Instances are the directions in which birds or insects fly after release and time-of-day viewed as a circular variable. In econometrics, season or month-of-the-year are discrete circular variables that correspond to angular portions of the earth's orbit around the sun. Section 1.1 recalls the definitions of random direction or random axis and of mean direction or mean axis. This paper develops nonparametric methods for comparing all pairs of mean directions (or mean axes) of \(s\) independent samples of directions (or axes). No shape assumptions are imposed upon the unknown distribution of the observations in each sample. In practice, a mean direction or a mean axis summarizes a distribution most effectively when that distribution is unimodal. Central to our methodology is the representation of the rotational difference between two mean directions (or two mean axes) as a direction (or axis). This representation has two important features: it enables us to apply nonparametric methods for inference about one mean direction or one mean axis, and it suggests plots for rotational differences in two or three dimensions. Details of the representation are the subject of Section 1.2. Section 2 constructs confidence sets for the rotational difference between the mean directions (or mean axes) of two samples. Simultaneous confidence sets for all pairwise rotational differences among the mean directions (or mean axes) of \(s\) samples are developed in Section 3. Section 4 illustrates our methodology on data.
Mathematics Subject Classification ID: 62H11
Mathematics Subject Classification ID: 62G10
Mathematics Subject Classification ID: 62G15
zbMATH DE Number: 1359522
zbMATH Keywords: simultaneous confidence sets
zbMATH Keywords: simultaneous tests
zbMATH Keywords: bootstrap
zbMATH Keywords: rotational difference
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1028144845
OpenAlex ID: W2014927261
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DOI: 10.1214/AOS/1028144845
description: scientific article; zbMATH DE number 1359522