Nonparametric depth and quantile regression for functional data

Chowdhury, Joydeep; Chaudhuri, Probal

doi:10.3150/17-bej991

Cited by 24 publications

(14 citation statements)

References 43 publications

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“…For the bivariate curves in the third row of Figure 10 Additional Applications Two applications on more generally structured functional data are demonstrated: the Cigarette data (Chowdhury and Chaudhuri, 2016) are four-dimensional functional data recorded on a one-dimensional time interval; image data from a video filmed by a static camera are three-dimensional functional data recorded on a two-dimensional space.…”

Section: Ms−plotmentioning

confidence: 99%

Multivariate Functional Data Visualization and Outlier Detection

Dai

Genton

2018

Journal of Computational and Graphical Statistics

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This paper proposes a new graphical tool, the magnitude-shape (MS) plot, for visualizing both the magnitude and shape outlyingness of multivariate functional data. The proposed tool builds on the recent notion of functional directional outlyingness, which measures the centrality of functional data by simultaneously considering the level and the direction of their deviation from the central region. The MS-plot intuitively presents not only levels but also directions of magnitude outlyingness on the horizontal axis or plane, and demonstrates shape outlyingness on the vertical axis. A dividing curve or surface is provided to separate non-outlying data from the outliers. Both the simulated data and the practical examples confirm that the MS-plot is superior to existing tools for visualizing centrality and detecting outliers for functional data.

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Section: Ms−plotmentioning

confidence: 99%

Multivariate Functional Data Visualization and Outlier Detection

Dai

Genton

2018

Journal of Computational and Graphical Statistics

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“…The success of spatial quantiles is partly explained by their ability to cope with high-dimensional data and even functional data; see, e.g., [3], [4], [5] and [6]. These quantiles were also used with much success to conduct multiple-output quantile regression, again also in the framework of functional data analysis; we refer to [7], [9], and [10]. The present work, however, focuses on the finite-dimensional case.…”

Section: Introductionmentioning

confidence: 99%

On the Behavior of Extreme d-dimensional Spatial Quantiles Under Minimal Assumptions

Paindaveine¹,

Virta

2021

Advances in Contemporary Statistics and Econometrics

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Spatial or geometric quantiles are the only multivariate quantiles coping with both high-dimensional data and functional data, also in the framework of multiple-output quantile regression. This work studies spatial quantiles in the finitedimensional case, where the spatial quantile µ α,u (P) of the distribution P taking values in R d is a point in R d indexed by an order α ∈ [0, 1) and a direction u in the unit sphere S d−1 of R d -or equivalently by a vector αu in the open unit ball of R d . Recently, [13] proved that (i) the extreme quantiles µ α,u (P) obtained as α → 1 exit all compact sets of R d and that (ii) they do so in a direction converging to u. These results help understanding the nature of these quantiles: the first result is particularly striking as it holds even if P has a bounded support, whereas the second one clarifies the delicate dependence of spatial quantiles on u. However, they were established under assumptions imposing that P is non-atomic, so that it is unclear whether they hold for empirical probability measures. We improve on this by proving these results under much milder conditions, allowing for the sample case. This prevents using gradient condition arguments, which makes the proofs very challenging. We also weaken the well-known sufficient condition for uniqueness of finite-dimensional spatial quantiles.

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“…Delicado and Vieu, 2017). In the one-dimensional case that we consider here, it is well known that the Wasserstein transport can also be expressed in terms of quantile functions (Hoeffding, 1940;Zhang and Müller, 2011;Chowdhury and Chaudhuri, 2019).…”

Section: Introductionmentioning

confidence: 99%

Wasserstein gradients for the temporal evolution of probability distributions

Chen

Müller

2021

Electron. J. Statist.

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Many studies have been conducted on flows of probability measures, often in terms of gradient flows. We utilize a generalized notion of derivatives with respect to time to model the instantaneous evolution of empirically observed one-dimensional distributions that vary over time and develop consistent estimates for these derivatives. Employing local Fréchet regression and working in local tangent spaces with regard to the Wasserstein metric, we derive the rate of convergence of the proposed estimators. The resulting time dynamics are illustrated with time-varying distribution data that include yearly income distributions and the evolution of mortality over calendar years.

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Nonparametric depth and quantile regression for functional data

Cited by 24 publications

References 43 publications

Multivariate Functional Data Visualization and Outlier Detection

Multivariate Functional Data Visualization and Outlier Detection

On the Behavior of Extreme d-dimensional Spatial Quantiles Under Minimal Assumptions

Wasserstein gradients for the temporal evolution of probability distributions

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