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Data depth functions are a generalization of one-dimensional order statistics and medians to real spaces of dimension greater than one; in particular, a data depth function quantifies the centrality of a point with respect to a data set or…

Statistics Theory · Mathematics 2016-05-17 Michael Burr , Robert Fabrizio

The concept of depth has proved very important for multivariate and functional data analysis, as it essentially acts as a surrogate for the notion a ranking of observations which is absent in more than one dimension. Motivated by the rapid…

Methodology · Statistics 2021-07-30 Gery Geenens , Alicia Nieto-Reyes , Giacomo Francisci

The $DD\alpha$-classifier, a nonparametric fast and very robust procedure, is described and applied to fifty classification problems regarding a broad spectrum of real-world data. The procedure first transforms the data from their original…

Applications · Statistics 2022-11-10 Pavlo Mozharovskyi , Karl Mosler , Tatjana Lange

Statistical depth, a commonly used analytic tool in non-parametric statistics, has been extensively studied for multivariate and functional observations over the past few decades. Although various forms of depth were introduced, they are…

Methodology · Statistics 2019-09-30 Weilong Zhao , Zishen Xu , Yun Yang , Wei Wu

During the past two decades there has been a lot of interest in developing statistical depth notions that generalize the univariate concept of ranking to multivariate data. The notion of depth has also been extended to regression models and…

Methodology · Statistics 2015-08-18 Peter J. Rousseeuw , Mia Hubert

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…

Methodology · Statistics 2020-09-23 Arthur Pewsey , Eduardo García-Portugués

Directional data consist of observations distributed on a (hyper)sphere, and appear in many applied fields, such as astronomy, ecology, and environmental science. This paper studies both statistical and computational problems of kernel…

Machine Learning · Statistics 2021-10-18 Yikun Zhang , Yen-Chi Chen

Data depths are score functions that quantify in an unsupervised fashion how central is a point inside a distribution, with numerous applications such as anomaly detection, multivariate or functional data analysis, arising across various…

Machine Learning · Statistics 2025-07-14 Arturo Castellanos , Pavlo Mozharovskyi

The direction of outlyingness is crucial to describing the centrality of multivariate functional data. Motivated by this idea, we generalize classical depth to directional outlyingness for functional data. We investigate theoretical…

Methodology · Statistics 2018-04-24 Wenlin Dai , Marc G. Genton

Statistical depth is the act of gauging how representative a point is compared to a reference probability measure. The depth allows introducing rankings and orderings to data living in multivariate, or function spaces. Though widely applied…

Statistics Theory · Mathematics 2021-05-28 George Wynne , Stanislav Nagy

One of the classic concerns in statistics is determining if two samples come from thesame population, i.e. homogeneity testing. In this paper, we propose a homogeneitytest in the context of Functional Data Analysis, adopting an idea from…

Applications · Statistics 2021-10-22 Alejandro Calle-Saldarriaga , Henry Laniado , Francisco Zuluaga

We propose a novel measure of statistical depth, the metric spatial depth, for data residing in an arbitrary metric space. The measure assigns high (low) values for points located near (far away from) the bulk of the data distribution,…

Statistics Theory · Mathematics 2023-06-19 Joni Virta

Directional data consists of unit vectors in q-dimensions that can be described in polar or Cartesian coordinates. Axial data can be viewed as a pair of directions pointed in opposite directions or as a projection matrix of rank 1.…

Methodology · Statistics 2025-10-22 Rudolf Beran

In real world, the huge amount of temporal data is to be processed in many application areas such as scientific, financial, network monitoring, sensor data analysis. Data mining techniques are primarily oriented to handle discrete features.…

Databases · Computer Science 2014-02-19 P. Chaudhari , D. P. Rana , R. G. Mehta , N. J. Mistry , M. M. Raghuwanshi

Data depth is an efficient tool for robustly summarizing the distribution of functional data and detecting potential magnitude and shape outliers. Commonly used functional data depth notions, such as the modified band depth and extremal…

Methodology · Statistics 2023-11-07 Cristian F. Jimenez-Varon , Fouzi Harrou , Ying Sun

The aim of ordinal classification is to predict the ordered labels of the output from a set of observed inputs. Interval-valued data refers to data in the form of intervals. For the first time, interval-valued data and interval-valued…

Methodology · Statistics 2023-11-06 Aleix Alcacer , Marina Martínez-Garcia , Irene Epifanio

In this article, we develop and investigate a new classifier based on features extracted using spatial depth. Our construction is based on fitting a generalized additive model to the posterior probabilities of the different competing…

Methodology · Statistics 2015-04-16 Subhajit Dutta , Anil K. Ghosh

The notion of a local fractional derivative (LFD) was introduced recently for functions of a single variable. LFD was shown to be useful in studying fractional differentiability properties of fractal and multifractal functions. It was…

Mathematical Physics · Physics 2008-11-06 Kiran M. Kolwankar , Anil D. Gangal

Anomaly detection is a branch of data analysis and machine learning which aims at identifying observations that exhibit abnormal behaviour. Be it measurement errors, disease development, severe weather, production quality default(s) (items)…

Machine Learning · Statistics 2024-07-11 Pavlo Mozharovskyi , Romain Valla

Data depth is a concept in multivariate statistics that measures the centrality of a point in a given data cloud in $\IR^d$. If the depth of a point can be represented as the minimum of the depths with respect to all one-dimensional…

Computation · Statistics 2020-07-17 Rainer Dyckerhoff , Pavlo Mozharovskyi , Stanislav Nagy