Objective Bayesian analysis for exponential power regression models

Salazar, Esther; Ferreira, Marco A. R.; Migon, Hélio S.

doi:10.1007/s13571-012-0045-0

Cited by 19 publications

(26 citation statements)

References 19 publications

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“…Specifically, the EPD is heavy-tailed distributions, if 1 < p < 2 and light-tailed distributions, if p > 2. Also, the special cases of the EPD are the double exponential distribution (p = 1), the normal distribution (p = 2) and the uniform distribution (p → ∞) as seen in Recently, many studies that consider the skewness as well as the kurtosis in view of robustness have been actively discussed (Zhu and Zinde-Walsh, 2009;DiCiccio and Monti, 2004;Salazar et al, 2012).…”

Section: Introductionmentioning

confidence: 99%

Robust Bayesian analysis for autoregressive models

Ryu¹,

Kim

2015

Journal of the Korean Data and Information Science Society

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Time series data sometimes show violation of normal assumptions. For cases where the assumption of normality is untenable, more flexible models can be adopted to accommodate heavy tails. The exponential power distribution (EPD) is considered as possible candidate for errors of time series model that may show violation of normal assumption. Besides, the use of flexible models for errors like EPD might be able to conduct the robust analysis. In this paper, we especially consider EPD as the flexible distribution for errors of autoregressive models. Also, we represent this distribution as scale mixture of uniform and this form enables efficient Bayesian estimation via Markov chain Monte Carlo (MCMC) methods.

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Section: Introductionmentioning

confidence: 99%

Robust Bayesian analysis for autoregressive models

Ryu¹,

Kim

2015

Journal of the Korean Data and Information Science Society

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“…Specifically, assuming an EP distribution decreases the influence of outliers and, as a result, increases the robustness of the analysis (Box and Tiao 1962;Liang et al 2007;Salazar et al 2012;West 1984). In addition, the EP distribution includes the Gaussian distribution as a particular case.…”

Section: Introductionmentioning

confidence: 99%

“…Platykurtic distributions may be a result of truncation, whereas leptokurtic distributions provide protection against outliers. Salazar et al (2012) have developed three types of Jeffreys priors for linear regression models with independent EP errors. Unfortunately, two of those priors lead to useless improper posterior distributions and only one leads to a proper posterior distribution.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, there are no published reference priors for EP regression models. Existing literature has considered the use of EP errors in a number of contexts such as, for example, EP errors to robustify linear models (Box and Tiao 1992;Salazar et al 2012), and mixtures of regression models with EP errors (Achcar and Pereira 1999). In addition, the EP distribution has been used as a prior for a Gaussian model location parameter (Choy and Smith 1997).…”

Section: Introductionmentioning

confidence: 99%

“…To implement simulation-based computation for models with EP errors, one may use representations of the EP distribution as a scale mixture of normals (West 1987) or as a scale mixture of uniforms (Walker and Gutiérrez-Peña 1999). As an alternative, Salazar et al (2012) have developed fast analysis for EP regression models using Laplace approximations and Newton-Cotes integration. Here we use these latter fast computational methods.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian reference analysis for exponential power regression models

Ferreira

Salazar

2014

J Stat Distrib Appl

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We develop Bayesian reference analyses for linear regression models when the errors follow an exponential power distribution. Specifically, we obtain explicit expressions for reference priors for all the six possible orderings of the model parameters and show that, associated with these six parameters orderings, there are only two reference priors. Further, we show that both of these reference priors lead to proper posterior distributions. Furthermore, we show that the proposed reference Bayesian analyses compare favorably to an analysis based on a competing noninformative prior. Finally, we illustrate these Bayesian reference analyses for exponential power regression models with applications to two datasets. The first application analyzes per capita spending in public schools in the United States. The second application studies the relationship between sold home videos versus profits at the box office. MSC: 62F15; 62F35; 62J05

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Bayesian analysis of two-piece location–scale models under reference priors with partial information

Wang

Sun

2016

Computational Statistics & Data Analysis

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Objective Bayesian analysis for exponential power regression models

Cited by 19 publications

References 19 publications

Robust Bayesian analysis for autoregressive models

Robust Bayesian analysis for autoregressive models

Bayesian reference analysis for exponential power regression models

Bayesian analysis of two-piece location–scale models under reference priors with partial information

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