Likelihood-Based Inference for Multivariate Skew-Normal Regression Models

Lachos, Víctor H.; Bolfarine, Heleno; Arellano–Valle, Reinaldo B.; Montenegro, Lourdes C.

doi:10.1080/03610920601126241

Cited by 64 publications

(55 citation statements)

References 23 publications

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“…, σ 2 e i ) and Z ∼ SN p (μ, , λ) denotes a p-variate skew-normal random vector with location vector μ, scale matrix and skewness parameter vector λ. For further details see [23]. From Proposition 6 in [7], it can be shown that ζ ij and x ij are independent with…”

Section: The Modelmentioning

confidence: 95%

“…If λ x = 0, then the asymmetric model reduces to the N-NIMEM. From the marginal stochastic representation of an SN random vector (see [23]), it follows that the regression set up defined in Equations (2), (3) can be written hierarchically as…”

Section: The Modelmentioning

confidence: 99%

“…For example, skew-t distributions [8], skew-Cauchy distributions [5], skew-slash distributions [28], skew-logistic distributions [27] and skew-elliptical distributions [10,19,25]. The use of the skew-normal distribution in our data set is motivated by the following considerations: (1) the unobserved covariate in a null measurement error model can have substantial non-normality, like skewness, which may not be captured by the routine use of normal distribution, (2) the histogram and corresponding Q-Q plot (Figure 1b) of the empirical Bayes estimates of the latent variable when normality is assumed shows that it is positively skewed and thus a Gaussian model does not fit well (see Section 4), (3) the skew-normal class defines an entire family and, as a special case, contains the normal distributions; (4) this generalisation is easy to implement and has the potential to make the inference robust to deviation from a normal distribution, and (5) the results presented in [23] do not consider the situation in which the slope parameter lies in the interval [0, 1].…”

Section: Introductionmentioning

confidence: 95%

See 2 more Smart Citations

Bayesian analysis for a skew extension of the multivariate null intercept measurement error model

Cancho

Aoki

Lachos

2008

Journal of Applied Statistics

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Skew-normal distribution is a class of distributions that includes the normal distributions as a special case. In this paper, we explore the use of Markov Chain Monte Carlo (MCMC) methods to develop a Bayesian analysis in a multivariate, null intercept, measurement error model [R. Aoki, H. Bolfarine, J.A. Achcar, and D. Leao Pinto Jr, Bayesian analysis of a multivariate null intercept error-in-variables regression model, J. Biopharm. Stat. 13(4) (2003b), pp. 763-771] where the unobserved value of the covariate (latent variable) follows a skew-normal distribution. The results and methods are applied to a real dental clinical trial presented in [A. Hadgu and G. Koch, Application of generalized estimating equations to a dental randomized clinical trial, J. Biopharm. Stat. 9 (1999), pp. 161-178].Skew-normal distribution, Gibbs algorithm, skewness, multivariate null intercepts model, measurement error,

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Section: The Modelmentioning

confidence: 95%

Section: The Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

See 1 more Smart Citation

Bayesian analysis for a skew extension of the multivariate null intercept measurement error model

Cancho

Aoki

Lachos

2008

Journal of Applied Statistics

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“…This class is a modified version of the multivariate skew-normal distribution, proposed by Azzalini and Dalla-Valle (1996). This form is more applicable in linear model context, for example Arellano-Valle et al (2005a) and Lachos et al (2007), respectively, had used it for analyzing skewnormal linear mixed model and multivariate skew-normal regression models. Also, Lin and Lee (2008) used this version for estimation and prediction in linear mixed models with skew-normal random effects for longitudinal data.…”

Section: Introductionmentioning

confidence: 98%

An ECM Estimation Approach for Analyzing Multivariate Skew-Normal Data with Dropout

Baghfalaki

Ganjali

2012

Communications in Statistics - Simulation and Computation

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In this article, an ECM algorithm is developed to obtain the maximum likelihood estimates of parameters where multivariate skew-normal distribution is used for analyzing longitudinal skewed normal regression data with dropout. A simulation study is performed to investigate the performance of the presented algorithm. Also, the methodology is illustrated through two applications and the results of proposed methodology are compared with ECM under multivariate normal assumption using AIC and BIC criteria. Standard errors of parameter estimates are obtained by asymptotic observed information matrix.

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“…Table 8, it is observed that the estimates differ slightly between the two models. Following Lachos et al [34], we propose selecting the best fit between N-LRM and SP-LRM by inspection of information criteria such as AIC and BIC (the preferred model is the one with the smallest value of the criterion). The AIC and BIC values shown at the bottom of Table 8 indicate that the SP-LRM outperforms the N-LRM.…”

Section: Application Of the Modelmentioning

confidence: 99%

Estimation of a linear model with two-parameter symmetric platykurtic distributed errors

Andargie

Rao

2013

J. Uncertain. Anal. Appl.

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Purpose: A linear regression model with Gaussian-distributed error terms is the most widely used method to describe the possible relationship between outcome and predictor variables. However, there are some drawbacks of Gaussian errors such as the distribution being mesokurtic. In many practical situations, the variables under study may not be mesokurtic but are platykurtic. Hence, to analyze this sort of platykurtic variables, a multiple regression model with symmetric platykurtic (SP) distributed errors is needed. In this paper, we introduce and develop a multiple linear regression model with symmetric platykurtic distributed errors for the first time.Methods: We used the methods of ordinary least squares (OLS) and maximum likelihood (ML) to estimate the model parameters. The properties of the ML estimators with respect to the symmetric platykurtic distributed errors are discussed. The model selection criteria such as Akaike information criteria (AIC) and Bayesian information criteria (BIC) for the models are used. The utility of the proposed model is demonstrated with both simulation and real-time data.Results: A comparative study of symmetric platykurtic linear regression model with the Gaussian model revealed that the former gives good fit to some data sets. The results also revealed that ML estimators are more efficient than OLS estimators in terms of the relative efficiency of the one-step-ahead forecast mean square error. Conclusions: The study shows that the symmetric platykurtic distribution serves as an alternative to the normal distribution. The developed model is useful for analyzing data sets arising from agricultural experiments, portfolio management, space experiments, and a wide range of other practical problems.

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Likelihood-Based Inference for Multivariate Skew-Normal Regression Models

Cited by 64 publications

References 23 publications

Bayesian analysis for a skew extension of the multivariate null intercept measurement error model

Bayesian analysis for a skew extension of the multivariate null intercept measurement error model

An ECM Estimation Approach for Analyzing Multivariate Skew-Normal Data with Dropout

Estimation of a linear model with two-parameter symmetric platykurtic distributed errors

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