The centred parametrization for the multivariate skew-normal distribution

Arellano–Valle, Reinaldo B.; Azzalini, Adelchi

doi:10.1016/j.jmva.2008.01.020

Cited by 111 publications

(122 citation statements)

References 13 publications

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“…For inference connected to a skew-normal distribution, Azzalini and Capitanio (1999) and Arellano-Valle and Azzalini (2008) pointed out that singularity arises in the information matrix when the skewness parameter approaches 0, thus breaking down estimation procedures. As a remedy, they suggested to adopt the so-called centered parameterization.…”

Section: Skew Normal Random Effectsmentioning

confidence: 99%

A weighted composite likelihood approach for analysis of survey data under two-level models

Yi¹,

Rao²

2017

STAT SINICA

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Multi-level models provide a convenient framework for analyzing data from survey samples with hierarchical structures. Inferential procedures that take account of survey design features are well established for single-level (or marginal) models. However, methods that are valid for general multi-level models are somewhat limited. This paper presents a unified method for two-level models, based on a weighted composite likelihood approach, that takes account of design features and provides valid inferences even for small sample sizes within level 2 units. The proposed method has broad applicability and is straightforward to implement. Empirical studies have demonstrated that the method performs well in estimating the model parameters. Moreover, this research has an important implication: it provides a particular scenario to showcase the unique merit of the composite likelihood method where the likelihood method would not work.

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Section: Skew Normal Random Effectsmentioning

confidence: 99%

A weighted composite likelihood approach for analysis of survey data under two-level models

Yi¹,

Rao²

2017

STAT SINICA

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“…As stated in the Introduction, normality is typically obtained from the GSN class at η 0 = 0 or equivalently τ 0 = |η 0 | = 0. Azzalini [20], Arellano-Valle and Azzalini [28] and Azzalini and Capitanio [23] recall the singularity of SN FIM at η = 0, preventing the asymptotic distribution of the above statistic tests. As suggested by Azzalini [20], a solution to recover the non-singularity of the information matrix under the symmetry hypothesis comes from the use of the so-called centered parametrization defined in terms of the mean, variance and the skewness parameters of the SN distribution (see also [28,29]).…”

Section: One-sample Case: Test For Normalitymentioning

confidence: 99%

Generalized Skew-Normal Negentropy and Its Application to Fish Condition Factor Time Series

Arellano–Valle

Contreras-Reyes

Stehlík

2017

Entropy

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Abstract:The problem of measuring the disparity of a particular probability density function from a normal one has been addressed in several recent studies. The most used technique to deal with the problem has been exact expressions using information measures over particular distributions. In this paper, we consider a class of asymmetric distributions with a normal kernel, called Generalized Skew-Normal (GSN) distributions. We measure the degrees of disparity of these distributions from the normal distribution by using exact expressions for the GSN negentropy in terms of cumulants. Specifically, we focus on skew-normal and modified skew-normal distributions. Then, we establish the Kullback-Leibler divergences between each GSN distribution and the normal one in terms of their negentropies to develop hypothesis testing for normality. Finally, we apply this result to condition factor time series of anchovies off northern Chile.

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“…Also, the information matrix is singular, thus regularity conditions are no longer satisfied. One consequence of this fact is that likelihood ratio statistics is no longer distributed according to the central chi-square distribution (Arellano-Valle & Azzalini 2008). …”

Section: Its Density Function Is Given Bymentioning

confidence: 99%

Asymmetric Regression Models Bernoulli/Log Proportional-Hazard Distribution

Martínez-Flórez¹,

Barrera²

2014

Rev. colomb. estad.

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In this paper we introduce a kind of asymmetric distribution for nonnegative data called log-proportional hazard distribution (LPHF). This new distribution is used to study an asymmetrical regression model for data with limited responses (censored) through the mixture of a Bernoulli distribution with logit link and the LPHF distribution. Properties of the LPHF distribution are studied, maximum likelihood parameter estimation and information matrices are addressed. An illustration with real data shows that the model is a new alternative for studies with positive data censored.Key words: Censoring, Fisher information matrix, Maximum likelihood estimators, Proportional hazard. ResumenEn este artículo se introduce una forma de distribución asimétrica para datos no-negativos llamada distribución log hazard proporcional (LPHF). Esta nueva distribución es usada para estudiar un modelo de regresión asimé-trico para datos con respuestas limitadas (censuradas) a través de mezclas de una distribución Bernoulli con función link logit y la distribución LPHF. Propiedades de la distribución LPHF son estudiadas, se abordan las estimaciones de máxima verosimilitud de los parámetros y las matrices de información. Se presenta una ilustración con datos reales, donde se muestra que el modelo propuesto es una nueva alternativa para estudios con datos positivos censurados.Palabras clave: censura, estimadores de máxima verosimilitud, hazard proporcional, matriz de información de Fisher.a Professor.

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The centred parametrization for the multivariate skew-normal distribution

Cited by 111 publications

References 13 publications

A weighted composite likelihood approach for analysis of survey data under two-level models

A weighted composite likelihood approach for analysis of survey data under two-level models

Generalized Skew-Normal Negentropy and Its Application to Fish Condition Factor Time Series

Asymmetric Regression Models Bernoulli/Log Proportional-Hazard Distribution

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