Nonparametric tests for circular regression

Alonso-Pena, María; Ameijeiras–Alonso, Jose; Crujeiras, Rosa M.

doi:10.1080/00949655.2020.1818243

Cited by 4 publications

(15 citation statements)

References 21 publications

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“…Also with the goal of obtaining a nonparametric estimator of

g(\cdot )

, Alonso‐Pena et al. (2023) considered the maximization of the circular local log‐likelihood function as a circular extension of the methods studied by Fan et al. (1998).…”

Section: Models For the Directional Tuning Of Spike Count Datamentioning

confidence: 99%

“…Analogously, a good selection of κ would make the choice of p less crucial. It is usually recommended (Alonso‐Pena et al., 2023; Fan & Gijbels, 1996) that if one wants to estimate

g^{(\nu )}(\theta _0)

, the choice

p=\nu +1

should be employed.…”

Section: Models For the Directional Tuning Of Spike Count Datamentioning

confidence: 99%

“…Note that the work by Alonso‐Pena et al. (2023) deals with the estimation of one conditional characteristic, while the present approach focuses on the simultaneous estimation of two conditional characteristics.…”

Section: Joint Estimation Through the Circular Local Likelihoodmentioning

confidence: 99%

“…Additionally, Section 5.3 introduces a graphical representation for the visualization of both estimated functions. The code used in this section can be found within the R package NPCirc (Alonso‐Pena et al., 2022) and also within the Supporting Information.…”

Section: Simulation Experimentsmentioning

confidence: 99%

“…First, Poisson models are considered: the parametric Poisson (PP) model in (2) and the nonparametric Poisson (NPP) studied by Alonso‐Pena et al. (2023). These approaches do not allow for the estimation of the dispersion function, since they assume that the value of the dispersion is always 1.…”

Section: Simulation Experimentsmentioning

confidence: 99%

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Flexible Joint Modeling of Mean and Dispersion for the Directional Tuning of Neuronal Spike Counts

2023

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The study of how the number of spikes in a middle temporal visual area (MT/V5) neuron is tuned to the direction of a visual stimulus has attracted considerable attention over the years, but recent studies suggest that the variability of the number of spikes might also be influenced by the directional stimulus. This entails that Poisson regression models are not adequate for this type of data, as the observations usually present over/underdispersion (or both) with respect to the Poisson distribution. This paper makes use of the double exponential family and presents a flexible model to estimate, jointly, the mean and dispersion functions, accounting for the effect of a circular covariate. The empirical performance of the proposal is explored via simulations and an application to a neurological data set is shown.

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“…Also with the goal of obtaining a nonparametric estimator of

g(\cdot )

, Alonso‐Pena et al. (2023) considered the maximization of the circular local log‐likelihood function as a circular extension of the methods studied by Fan et al. (1998).…”

Section: Models For the Directional Tuning Of Spike Count Datamentioning

confidence: 99%

“…Analogously, a good selection of κ would make the choice of p less crucial. It is usually recommended (Alonso‐Pena et al., 2023; Fan & Gijbels, 1996) that if one wants to estimate

g^{(\nu )}(\theta _0)

, the choice

p=\nu +1

should be employed.…”

Section: Models For the Directional Tuning Of Spike Count Datamentioning

confidence: 99%

Section: Joint Estimation Through the Circular Local Likelihoodmentioning

confidence: 99%

Section: Simulation Experimentsmentioning

confidence: 99%

Section: Simulation Experimentsmentioning

confidence: 99%

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Flexible Joint Modeling of Mean and Dispersion for the Directional Tuning of Neuronal Spike Counts

2023

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Recent advances in directional statistics

Pewsey

García‐Portugués

2021

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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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