A new family of multivariate heavy-tailed distributions with variable marginal amounts of tailweight: application to robust clustering

Forbes, Florence; Wraith, Darren

doi:10.1007/s11222-013-9414-4

Cited by 101 publications

(88 citation statements)

References 31 publications

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“…In addition, even in the case of quantitative data, the Gaussian assumption may not be well-suited for the data at hand. Recent works focused on different distributions such as the skew normal (Lin et al 2007), asymmetric Laplace (Franczak et al 2014) or t-distributions (Andrews and McNicholas 2012;Lee and McLachlan 2013;Lin 2010;Forbes and Wraith 2014).…”

Section: Model-based Classificationmentioning

confidence: 99%

Kernel discriminant analysis and clustering with parsimonious Gaussian process models

Bouveyron¹,

Fauvel²,

Girard³

2014

Stat Comput

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International audienceThis work presents a family of parsimonious Gaussian process models which allow to build, from a finite sample, a model-based classifier in an infinite dimensional space. The proposed parsimonious models are obtained by constraining the eigen-decomposition of the Gaussian processes modeling each class. This allows in particular to use non-linear mapping functions which project the observations into infinite dimensional spaces. It is also demonstrated that the building of the classifier can be directly done from the observation space through a kernel function. The proposed classification method is thus able to classify data of various types such as categorical data, functional data or networks. Furthermore, it is possible to classify mixed data by combining different kernels. The methodology is as well extended to the unsupervised classification case. Experimental results on various data sets demonstrate the effectiveness of the proposed method

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Section: Model-based Classificationmentioning

confidence: 99%

Kernel discriminant analysis and clustering with parsimonious Gaussian process models

Bouveyron¹,

Fauvel²,

Girard³

2014

Stat Comput

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“…Figure 3 in [34] represents a sample cloud which might be modeled with a density being star-shaped w.r.t. a fan having six cones that include sample points and other cones that do not.…”

Section: Applicationsmentioning

confidence: 99%

Estimation of Star-Shaped Distributions

Liebscher

Richter

2016

Risks

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Scatter plots of multivariate data sets motivate modeling of star-shaped distributions beyond elliptically contoured ones. We study properties of estimators for the density generator function, the star-generalized radius distribution and the density in a star-shaped distribution model. For the generator function and the star-generalized radius density, we consider a non-parametric kernel-type estimator. This estimator is combined with a parametric estimator for the contours which are assumed to follow a parametric model. Therefore, the semiparametric procedure features the flexibility of nonparametric estimators and the simple estimation and interpretation of parametric estimators. Alternatively, we consider pure parametric estimators for the density. For the semiparametric density estimator, we prove rates of uniform, almost sure convergence which coincide with the corresponding rates of one-dimensional kernel density estimators when excluding the center of the distribution. We show that the standardized density estimator is asymptotically normally distributed. Moreover, the almost sure convergence rate of the estimated distribution function of the star-generalized radius is derived. A particular new two-dimensional distribution class is adapted here to agricultural and financial data sets.

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“…Following the same approach as in Forbes and Wraith (2014), the standard location and scale representation (1) is generalized into a multiple scale version…”

Section: Multiple Scaled Generalized Hyperbolic Distribution (Msgh)mentioning

confidence: 99%

“…There have been various approaches to address this issue in the statistics literature for both symmetric and asymmetric distributional forms but most of them suffer either from the non-existence of a closed-form pdf or from a difficult generalization to more than two dimensions (see Forbes and Wraith, 2014 for more detailed references).…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we build upon the multiple scaled framework of Forbes and Wraith (2014) to provide a much wider variety of distributional forms, allowing different tail and skewness behaviour in each dimension of the variable space with arbitrary correlation between dimensions. A similar approach to ours has been undertaken in (as yet) unpublished work (Tortora et al, 2014b;Franczak et al, 2014).…”

Section: Introductionmentioning

confidence: 99%

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Location and scale mixtures of Gaussians with flexible tail behaviour: Properties, inference and application to multivariate clustering

Wraith

Forbes

2015

Computational Statistics & Data Analysis

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International audienceThe family of location and scale mixtures of Gaussians has the ability to generate a number of flexible distributional forms. The family nests as particular cases several important asymmetric distributions like the Generalized Hyperbolic distribution. The Generalized Hyperbolic distribution in turn nests many other well known distributions such as the Normal Inverse Gaussian. In a multivariate setting, an extension of the standard location and scale mixture concept is proposed into a so called multiple scaled framework which has the advantage of allowing different tail and skewness behaviours in each dimension with arbitrary correlation between dimensions. Estimation of the parameters is provided via an EM algorithm and extended to cover the case of mixtures of such multiple scaled distributions for application to clustering. Assessments on simulated and real data confirm the gain in degrees of freedom and flexibility in modelling data of varying tail behaviour and directional shape

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A new family of multivariate heavy-tailed distributions with variable marginal amounts of tailweight: application to robust clustering

Cited by 101 publications

References 31 publications

Kernel discriminant analysis and clustering with parsimonious Gaussian process models

Kernel discriminant analysis and clustering with parsimonious Gaussian process models

Estimation of Star-Shaped Distributions

Location and scale mixtures of Gaussians with flexible tail behaviour: Properties, inference and application to multivariate clustering

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