Recent advances in directional statistics

Arthur Pewsey () and Eduardo García-Portugués ()
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Arthur Pewsey: University of Extremadura
Eduardo García-Portugués: Carlos III University of Madrid

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2021, vol. 30, issue 1, No 1, 58 pages

Abstract: Abstract 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. An overview of currently available software for analysing directional data is also provided, and potential future developments are discussed.

Keywords: Classification; Clustering; Dimension reduction; Distributional models; Exploratory data analysis; Hypothesis tests; Nonparametric methods; Regression; Serial dependence; Software; Spatial statistics; 62H11 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (11)

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DOI: 10.1007/s11749-021-00759-x

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