Supersmooth testing on the sphere over analytic classes

Kim, Peter T.; Koo, Ja−Yong; Ngoc, Thanh Mai Pham

doi:10.1080/10485252.2015.1113284

Cited by 6 publications

(5 citation statements)

References 24 publications

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“…Now, the problem of testing uniformity over the unit sphere is primarily of a nonparametric nature. Even if the distributional framework described in Section 2 is considered, it is therefore valid to adopt a nonparametric point of view and to try to identify, e.g., minimax separation rates; see, e.g., Ingster (2000) or, in a directional context, Faÿ et al (2013), Lacour and Ngoc (2014) and Kim, Koo and Ngoc (2016). This approach is fundamentally different from the semiparametric one adopted in this work.…”

Section: Discussionmentioning

confidence: 98%

Testing uniformity on high-dimensional spheres against monotone rotationally symmetric alternatives

Cutting¹,

Paindaveine²,

Verdebout³

2017

Ann. Statist.

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We consider the problem of testing uniformity on high-dimensional unit spheres. We are primarily interested in non-null issues. We show that rotationally symmetric alternatives lead to two Local Asymptotic Normality (LAN) structures. The first one is for fixed modal location θ θ θ and allows to derive locally asymptotically most powerful tests under specified θ θ θ. The second one, that addresses the Fisher-von Mises-Langevin (FvML) case, relates to the unspecified-θ θ θ problem and shows that the high-dimensional Rayleigh test is locally asymptotically most powerful invariant. Under mild assumptions, we derive the asymptotic non-null distribution of this test, which allows to extend away from the FvML case the asymptotic powers obtained there from Le Cam's third lemma. Throughout, we allow the dimension p to go to infinity in an arbitrary way as a function of the sample size n. Some of our results also strengthen the local optimality properties of the Rayleigh test in low dimensions. We perform a Monte Carlo study to illustrate our asymptotic results. Finally, we treat an application related to testing for sphericity in high dimensions.

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Section: Discussionmentioning

confidence: 98%

Testing uniformity on high-dimensional spheres against monotone rotationally symmetric alternatives

Cutting¹,

Paindaveine²,

Verdebout³

2017

Ann. Statist.

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“…Tests for uniformity on S d include that of Faÿ et al (2013), based on needlets (see Sect. 7.1.2), and those of Lacour and Pham Ngoc (2014) and Kim et al (2016) for "noisy" data on S 2 , i.e. where the density of the observations is a convolution of an error pdf with a true underlying pdf.…”

Section: Uniformitymentioning

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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“…Recent non-Sobolev tests for circular uniformity include the four-point Cramér-von Mises test of Feltz and Goldin (2001), the likelihood-ratio test (LRT) against a mixture with symmetric wrapped stable and CU components of SenGupta and Pal (2001), and the spacings-based Gini mean difference test of Tung and Jammalamadaka (2013). Tests for uniformity on S d include that of Faÿ et al (2013), based on needlets (see Section 7.1.2), and those of Lacour and Pham Ngoc (2014) and Kim et al (2016) for noisy data on S 2 . Cuesta-Albertos et al ( 2009…”

Section: Uniformitymentioning

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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Supersmooth testing on the sphere over analytic classes

Cited by 6 publications

References 24 publications

Testing uniformity on high-dimensional spheres against monotone rotationally symmetric alternatives

Testing uniformity on high-dimensional spheres against monotone rotationally symmetric alternatives

Recent advances in directional statistics

Recent advances in directional statistics

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