Small nonparametric tolerance regions for directional data

Mushkudiani, NA Nino

doi:10.1016/s0378-3758(01)00093-3

Cited by 7 publications

(3 citation statements)

References 15 publications

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“…Pandolfo et al (2018b) introduced computationally tractable distance-based depths on S d , illustrating their use in location estimation and classification. A nonparametric approach to constructing tolerance regions for spherical data was proposed by Mushkudiani (2002).…”

Section: Statistical Depthmentioning

confidence: 99%

Recent advances in directional statistics

Pewsey

García‐Portugués

2021

TEST

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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: Statistical Depthmentioning

confidence: 99%

Recent advances in directional statistics

Pewsey

García‐Portugués

2021

TEST

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“…Recently, Pandolfo et al (2018b) introduced computationally tractable distancebased depths on S d , illustrating their use in location estimation and classification. A nonparametric approach to constructing tolerance regions for spherical data was proposed by Mushkudiani (2002).…”

Section: Statistical Depthmentioning

confidence: 99%

Recent advances in directional statistics

Pewsey¹,

García‐Portugués²

2020

Preprint

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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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“…For application to multivariate normal goodness-of-fit, see BEIRLANT, MASON and VYNCTIER (1999). For applications to obtain smallest volume nonparametric multivariate tolerance regions, see MUSHKUDIANI (2000), DI BUCCHIANICO, EINMAHL andMUSHKUDIANI (2001), andMUSHKUDIANI (2001). Further, as pointed out in MUSHKUDIANI (2000, }5.2.4), notions of multivariate P-P and Q-Q plots given by POLONIK (1999) as C-C plots may be based on generalized quantile functions.…”

Section: A ''Generalized Quantile'' Approachmentioning

confidence: 99%

Quantile functions for multivariate analysis: approaches and applications

Serfling¹

2002

Statistica Neerlandica

174

101

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Despite the absence of a natural ordering of Euclidean space for dimensions greater than one, the effort to define vector-valued quantile functions for multivariate distributions has generated several approaches. To support greater discrimination in comparing, selecting and using such functions, we introduce relevant criteria, including a notion of ''medianoriented quantile function''. On this basis we compare recent quantile approaches and several multivariate versions of trimmed mean and interquartile range. We also discuss a univariate ''generalized quantile'' approach that enables particular features of multivariate distributions, for example scale and kurtosis, to be studied by two-dimensional plots. Methods based on statistical depth functions are found to be especially attractive for quantile-based multivariate inference.

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Small nonparametric tolerance regions for directional data

Cited by 7 publications

References 15 publications

Recent advances in directional statistics

Recent advances in directional statistics

Recent advances in directional statistics

Quantile functions for multivariate analysis: approaches and applications

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