Shape mixtures of multivariate skew-normal distributions

Arellano–Valle, Reinaldo B.; Genton, Marc G.; Loschi, Rosangela H.

doi:10.1016/j.jmva.2008.03.009

Cited by 38 publications

(28 citation statements)

References 13 publications

(30 reference statements)

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“…The issue is that our greedy extraction of polynomial limits for the system (65) treats each equation of the system separately. For instance, in system (67), a special case of system (65) when r = 3, we do not consider the interaction between two summations 3 in the numerator of the second limit. As a result, the limiting polynomials obtained are dependent only on the lowest order monomial terms that appear in the numerator of each of the (r, r, r)-minimal form's coefficients.…”

Section: Behavior Of System Of Limiting Polynomial Equationsmentioning

confidence: 99%

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Singularity Structures and Impacts on Parameter Estimation in Finite Mixtures of Distributions

Ho¹,

Nguyen²

2019

SIAM Journal on Mathematics of Data Science

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Singularities of a statistical model are the elements of the model's parameter space which make the corresponding Fisher information matrix degenerate. These are the points for which estimation techniques such as the maximum likelihood estimator and standard Bayesian procedures do not admit the root-n parametric rate of convergence. We propose a general framework for the identification of singularity structures of the parameter space of finite mixtures, and study the impacts of the singularity structures on minimax lower bounds and rates of convergence for the maximum likelihood estimator over a compact parameter space. Our study makes explicit the deep links between model singularities, parameter estimation convergence rates and minimax lower bounds, and the algebraic geometry of the parameter space for mixtures of continuous distributions. The theory is applied to establish concrete convergence rates of parameter estimation for finite mixture of skew-normal distributions. This rich and increasingly popular mixture model is shown to exhibit a remarkably complex range of asymptotic behaviors which have not been hitherto reported in the literature. 1

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Section: Behavior Of System Of Limiting Polynomial Equationsmentioning

confidence: 99%

“…Hence, there are 13 variables with only 7 equations. If we choose d 1 = d 2 = d 3 and take the lexicographical ordering a 1 ≻ a 2 ≻ a 3…”

mentioning

confidence: 99%

Singularity Structures and Impacts on Parameter Estimation in Finite Mixtures of Distributions

Ho¹,

Nguyen²

2019

SIAM Journal on Mathematics of Data Science

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“…The idea of shape mixture of a skew-symmetric distributions is introduced by Arellano- , (see also Arellano-Valle et al (2009)) and is applied by Arrue et al (2011) to the univariate SNC distribution. Following Genton and Loperfido (2005), the multivariate SNC distribution is defined as follows.…”

Section: Multivariate Skew-normal-cauchy Distributionmentioning

confidence: 99%

On the multivariate skew-normal-Cauchy distribution

Kahrari

Rezaei

Yousefzadeh

et al. 2016

Statistics & Probability Letters

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“…For example, the percentage points of distribution of X (3) and the cdf of X (2) are presented in Tables 1 and 2, when ρ = 1 2 .…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Properties and Inference for a New Class of Skew-t Distributions

Roozegar

Nematollahi

Jamalizadeh

2014

Communications in Statistics - Simulation and Computation

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In this paper we introduce a new generalization of skew-t distributions which contains the standard skew-t distribution, as a special case. This new class of distributions is an adequate model for modeling some data set rather than to the standard skew-t distributions. This kind of distributions can be represented as a scale-shape mixture of the extended skew normal distributions. The main properties of this family of distributions are studied and a recurrence relation for the cdf of them is presented. We derive the distribution of the order statistics from the trivariate exchangeable t-distribution in terms of our distribution and then an exact expression for the cdf of order statistics is derived. Likelihood inference for this distribution is also examined. The method is illustrated with a numerical example via a simulation study.

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Shape mixtures of multivariate skew-normal distributions

Cited by 38 publications

References 13 publications

Singularity Structures and Impacts on Parameter Estimation in Finite Mixtures of Distributions

Singularity Structures and Impacts on Parameter Estimation in Finite Mixtures of Distributions

On the multivariate skew-normal-Cauchy distribution

Properties and Inference for a New Class of Skew-t Distributions

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