Identifiability of Finite Mixtures of Elliptical Distributions

By Hajo Holzmann, Axel Munk, Tilmann Gneiting. 2006

108 citations recorded by the source corpus.

Abstract. We present general results on the identifiability of finite mixtures of elliptical distributions under conditions on the characteristic generators or density generators. Examples include the multivariate t‐distribution, symmetric stable laws, exponential power and Kotz distributions. In each case, the shape parameter is allowed to vary in the mixture, in addition to the location vector and the scatter matrix. Furthermore, we discuss the identifiability of finite mixtures of elliptical densities with generators that correspond to scale mixtures of normal distributions.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/94a326afe42348b3efeff00bb6489194195b24f8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Statistics and Probability

Citations in the corpus

Local Proper Scoring Rules (2009, background): “are bounded as |x| → ∞. The class Pα is very general and includes elliptically symmetric normal, Student’s t and related densities ( Holzmann, Munk and Gneiting 2006 ), the respective skew-elliptical densities (Genton 2004), and finite mixtures of the above, among many other densities of applied or ”
Consistency of mixture models with a prior on the number of components (2022, methodology): “For Fv, the family of component distributions, there are many commonly used choices that satisfy Condition 2.1(2), including the multivariate normal (Yakowitz and Spragins, 1968) and, more generally, many elliptical families such as the multivariate t distributions (Holzmann et al., 2006).”
Bayesian Subset Modeling for High-Dimensional Generalized Linear Models (2013, background): “The identifiability of (22) was established in Holzmann, Munk, and Gneiting (2006).”
A mixture of generalized hyperbolic distributions (2013, methodology): “Now, with this ground work having been laid down, the proof follows similarly to Theorem 1 in Holzmann et al. (2006). Starting with a dependence relation like in (14), but assuming that f ∈ G(α,δ) and applying the Fourier transform, we obtain”