Skew-Elliptical Distributions and Their Applications : A Journey Beyond Normality
27 Jul 2004-
TL;DR: This book reviews the state-of-the-art advances in skew-elliptical distributions and provides many new developments in a single volume, collecting theoretical results and applications previously scattered throughout the literature.
Abstract: This book reviews the state-of-the-art advances in skew-elliptical distributions and provides many new developments in a single volume, collecting theoretical results and applications previously scattered throughout the literature. The main goal of this research area is to develop flexible parametric classes of distributions beyond the classical normal distribution. The book is divided into two parts. The first part discusses theory and inference for skew-elliptical distribution. The second part presents applications and case studies in areas such as economics, finance, oceanography, climatology, environmetrics, engineering, image processing, astronomy, and biomedical science.
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TL;DR: In this paper, the authors provide an introductory overview of a portion of distribution theory which is currently under intense development and illustrate connections with various areas of application, including selective sampling, models for compositional data, robust methods, some problems in econometrics, non-linear time series, especially in connection with financial data, and more.
Abstract: . This paper provides an introductory overview of a portion of distribution theory which is currently under intense development. The starting point of this topic has been the so-called skew-normal distribution, but the connected area is becoming increasingly broad, and its branches include now many extensions, such as the skew-elliptical families, and some forms of semi-parametric formulations, extending the relevance of the field much beyond the original theme of ‘skewness’. The final part of the paper illustrates connections with various areas of application, including selective sampling, models for compositional data, robust methods, some problems in econometrics, non-linear time series, especially in connection with financial data, and more.
657 citations
Cites background from "Skew-Elliptical Distributions and T..."
...This important problem has been examined byWang et al. (2004) and Ma & Genton (2004), whose results can be summarized as follows; in their formulation, the term Gfw(x)g in (12) is replaced by the perturbation function p(x), satisfying conditions (14)....
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...Luckily, quite a few of them are collected in the recent book edited by Genton (2004a), hence accessible collectively....
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...Methods where p(x) is handled non-parametrically have been examined by Loperfido (2004) and by Genton 2004b, section 5.4.3)....
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25 Apr 2010
TL;DR: This work presents a direct multivariate finite mixture modeling approach, using skew and heavy-tailed distributions, to address the complexities of flow cytometric analysis and to deal with high-dimensional cytometric data without the need for projection or transformation.
Abstract: Flow cytometry is widely used for single cell interrogation of surface and intracellular protein expression by measuring fluorescence intensity of fluorophore-conjugated reagents We focus on the recently developed procedure of Pyne et al (2009, Proceedings of the National Academy of Sciences USA 106, 8519-8524) for automated high- dimensional flow cytometric analysis called FLAME (FLow analysis with Automated Multivariate Estimation) It introduced novel finite mixture models of heavy-tailed and asymmetric distributions to identify and model cell populations in a flow cytometric sample This approach robustly addresses the complexities of flow data without the need for transformation or projection to lower dimensions It also addresses the critical task of matching cell populations across samples that enables downstream analysis It thus facilitates application of flow cytometry to new biological and clinical problems To facilitate pipelining with standard bioinformatic applications such as high-dimensional visualization, subject classification or outcome prediction, FLAME has been incorporated with the GenePattern package of the Broad Institute Thereby analysis of flow data can be approached similarly as other genomic platforms We also consider some new work that proposes a rigorous and robust solution to the registration problem by a multi-level approach that allows us to model and register cell populations simultaneously across a cohort of high-dimensional flow samples This new approach is called JCM (Joint Clustering and Matching) It enables direct and rigorous comparisons across different time points or phenotypes in a complex biological study as well as for classification of new patient samples in a more clinical setting.
354 citations
TL;DR: In this article, the authors unify these proposals under a new general formulation, clarifying at the same time their relationships, and sketch an extension of the argument to the skew-elliptical family.
Abstract: . The distribution theory literature connected to the multivariate skew-normal distribution has grown rapidly in recent years, and a number of extensions and alternative formulations have been put forward. Presently there are various coexisting proposals, similar but not identical, and with rather unclear connections. The aim of this paper is to unify these proposals under a new general formulation, clarifying at the same time their relationships. The final part sketches an extension of the argument to the skew-elliptical family.
348 citations
Cites background from "Skew-Elliptical Distributions and T..."
...For reviews of the research work produced in this area, see Arnold & Beaver (2002), Genton (2004) and Azzalini (2005)....
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TL;DR: In this article, a new class of multivariate skew-normal distributions, fundamental skew normal distributions, and their canonical version, is developed, which contains the product of independent univariate skewnormal distributions as a special case.
329 citations
TL;DR: In this paper, the robustness problem is tackled by adopting a parametric class of distributions flexible enough to match the behaviour of the observed data, and the skew-t distribution is explored in more detail and reasons to adopt this option as a sensible general-purpose compromise between robustness and simplicity, both of treatment and interpretation of the outcome.
Abstract: Summary
The robustness problem is tackled by adopting a parametric class of distributions flexible enough to match the behaviour of the observed data. In a variety of practical cases, one reasonable option is to consider distributions which include parameters to regulate their skewness and kurtosis. As a specific representative of this approach, the skew-t distribution is explored in more detail and reasons are given to adopt this option as a sensible general-purpose compromise between robustness and simplicity, both of treatment and of interpretation of the outcome. Some theoretical arguments, outcomes of a few simulation experiments and various wide-ranging examples with real data are provided in support of the claim.
Resume
Le probleme de la robustesse est attaque en adoptant une classe parametrique de distributions qui sont suffisamment flexibles pour representer le comportement des observations. Dans une variete de cas pratiques, une option raisonnable est de considerer des distributions qui incluent des parametres pour regler leur asymetrie et leur aplatissement. Comme representant specifique de cette approche, la distribution t asymetrique est exploree plus en detail et des raisons sont apportees pour adopter cette option comme un compromis judicieux et a tous usages entre la robustesse et la simplicite du traitement et de l'interpretation des resultats. Quelques arguments theoriques, les resultats de simulations et divers exemples sur des donnees reelles sont fournis afin de soutenir cette affirmation.
234 citations