Multivariate measurement error models based on scale mixtures of the skew–normal distribution

Lachos, Víctor H.; Labra, Filidor V.; Bolfarine, Heleno; Ghosh, Pulak

doi:10.1080/02331880903236926

“…They proposed a simple method for obtaining consistent estimators, based on the corrected score approach. More recently, Lachos et al (2010c) have introduced MEM with scale mixtures of skew-normal distributions (SMSN-MEM) and presented a complete likelihood based analysis, including an efficient EM algorithm for maximum likelihood estimation.…”

Section: Introductionmentioning

confidence: 99%

“…The violation of this assumption can have adverse consequences for the efficiency of estimators (Cook and Weisberg 1982), so it is important to detect the variance heterogeneity in MEM. Motived by the work of Lachos et al (2010c), in this paper we discuss the local influence analysis and a score test statistic for assessing homogeneity of the skewness parameter, which is a parameter included in the variance, in SMSN-MEM. Since the observed log-likelihood function of SMSN models involves some integrals, a direct application of Cook's (1986) local influence approach can be very difficult to apply, because these measures involve the first and second partial derivatives of the log-likelihood function.…”

Section: Introductionmentioning

confidence: 99%

On diagnostics in multivariate measurement error models under asymmetric heavy-tailed distributions

Zeller

¹

,

Carvalho

²

,

Lachos

³

2011

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In this paper, we discuss the extension of some diagnostic procedures to multivariate measurement error models with scale mixtures of skew-normal distributions (Lachos et al., Statistics 44:541-556, 2010c). This class provides a useful generalization of normal (and skew-normal) measurement error models since the random term distributions cover symmetric, asymmetric and heavy-tailed distributions, such as skew-t, skew-slash and skew-contaminated normal, among others. Inspired by the EM algorithm proposed by Lachos et al. (Statistics 44:541-556, 2010c), we develop a local influence analysis for measurement error models, following Zhu and Lee's (J R Stat Soc B 63:111-126, 2001) approach. This is because the observed data loglikelihood function associated with the proposed model is somewhat complex and Cook's well-known approach can be very difficult to apply to achieve local influence measures. Some useful perturbation schemes are also discussed. In addition, a score test for assessing the homogeneity of the skewness parameter vector is presented. Finally, the methodology is exemplified through a real data set, illustrating the usefulness of the proposed methodology.

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“…The LLFT model has been used in survival analysis as a parametric model for mortality rate, hydrology, and networked telerobots (see, e.g., [20]). Following the same procedure as in [17], we can construct new robust FT models through differing designations of κ(η) and the distribution of η. Particularly, in the regulation of tail distribution in the FT model, a log-slash failure time (LSFT) model can be obtained by taking κ(η) = η −1 and η ∼ Beta(1/2, 1)-that is Beta distribution.…”

Section: The Class Of Smlnft Modelsmentioning

confidence: 99%

Bayesian Hierarchical Scale Mixtures of Log-Normal Models for Inference in Reliability with Stochastic Constraint

Kim

¹

2017

Entropy

1

0

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This paper develops Bayesian inference in reliability of a class of scale mixtures of log-normal failure time (SMLNFT) models with stochastic (or uncertain) constraint in their reliability measures. The class is comprehensive and includes existing failure time (FT) models (such as log-normal, log-Cauchy, and log-logistic FT models) as well as new models that are robust in terms of heavy-tailed FT observations. Since classical frequency approaches to reliability analysis based on the SMLNFT model with stochastic constraint are intractable, the Bayesian method is pursued utilizing a Markov chain Monte Carlo (MCMC) sampling based approach. This paper introduces a two-stage maximum entropy (MaxEnt) prior, which elicits a priori uncertain constraint and develops Bayesian hierarchical SMLNFT model by using the prior. The paper also proposes an MCMC method for Bayesian inference in the SMLNFT model reliability and calls attention to properties of the MaxEnt prior that are useful for method development. Finally, two data sets are used to illustrate how the proposed methodology works.

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“…The LLFT model has been used in survival analysis as a parametric model for mortality rate, hydrology, and networked telerobots (see, e.g., [19]). Following the same procedure as in [20,21], we can construct new robust FT models through differing designations of κ(η) and the distribution of η. Particularly, in the regulation of tail distribution in the FT model, a log-slash failure time (LSFT) model can be obtained by taking κ(η) = η −1 and η ∼ Beta(1/2, 1); that is Beta distribution.…”

Section: Of 15mentioning

confidence: 99%

Bayesian Hierarchical Scale Mixtures of Log-Normal Models for Inference in Reliability with Stochastic Constraint

Kim¹

2017

Preprint

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This paper develops Bayesian inference in reliability of a class of scale mixtures of log-normal failure time (SMLNFT) models with stochastic (or uncertain) constraint in their reliability measures. The class is comprehensive and includes existing failure time (FT) models (such as log-normal, log-Cauchy, and log-logistic FT models) as well as new models that are robust in terms of heavy-tailed FT observations. Since classical frequency approaches to reliability analysis based on the SMLNFT model with stochastic constraint are intractable, the Bayesian method is pursued utilizing a Markov chain Monte Carlo (MCMC) sampling based approach. This paper introduces a two-stage maximum entropy (MaxEnt) prior, which elicits a priori uncertain constraint and develops Bayesian hierarchical SMLNFT model by using the prior. The paper also proposes an MCMC method for Bayesian inference in the SMLNFT model reliability and calls attention to properties of the MaxEnt prior that are useful for method development. Finally, two data sets are used to illustrate how the proposed methodology works.

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Multivariate measurement error models based on scale mixtures of the skew–normal distribution

Cited by 42 publications

References 23 publications

On diagnostics in multivariate measurement error models under asymmetric heavy-tailed distributions

On diagnostics in multivariate measurement error models under asymmetric heavy-tailed distributions

Bayesian Hierarchical Scale Mixtures of Log-Normal Models for Inference in Reliability with Stochastic Constraint

Bayesian Hierarchical Scale Mixtures of Log-Normal Models for Inference in Reliability with Stochastic Constraint

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