A new test of discordancy in cylindrical data

Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere, and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper, we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (Wiley 1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, space situational awareness, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. AnWe are most grateful to three anonymous referees and, in alphabetical order, to

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Section: Outlier Detectionmentioning

confidence: 99%

Recent advances in directional statistics

Pewsey

García‐Portugués

2021

TEST

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“…Sau and Rodriguez (2018) developed a minimum distance approach to estimating the parameters of spherical models that provides an outlier detection tool. Outlier detection tests for cylindrical, simple circular regression, and circular time series data were proposed in Sadikon et al (2019), Abuzaid et al (2013), and Abuzaid et al (2014, respectively. Eigenvalue, LRT, and geodesic distance-based tests for detecting outliers in axial data from an assumed underlying Watson distribution were developed in Figueiredo and Gomes (2005), Figueiredo (2007), and Barros et al (2017).…”

Section: Outlier Detectionmentioning

confidence: 99%

Recent advances in directional statistics

Pewsey¹,

García‐Portugués²

2020

Preprint

View full text Add to dashboard Cite

Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial, and spatio-temporal data. We end with an overview of presently available software for analyzing directional data.

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