Normality and independence of error terms is a typical assumption for partial linear models. However, such an assumption may be unrealistic on many fields such as economics, finance and biostatistics. In this paper, we develop a Bayesian analysis for partial linear model with first-order autoregressive errors belonging to the class of scale mixtures of normal (SMN) distributions. The proposed model provides a useful generalization of the symmetrical linear regression models with independent error, since the error distribution cover both correlated and thick-tailed distribution, and has a convenient hierarchical representation allowing to us an easily implementation of a Markov chain Monte Carlo (MCMC) scheme. In order to examine the robustness of this distribution against outlying and influential observations, we present a Bayesian case deletion influence diagnostics based on the Kullback-Leibler (K-L) divergence. The proposed methodology is applied to the Cuprum Company monthly returns.
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18 October 2012
XI BRAZILIAN MEETING ON BAYESIAN STATISTICS: EBEB 2012
18–22 March 2012
Amparo‐SP, Brazil
Research Article|
October 18 2012
Partially linear models with autoregressive scale-mixtures of normal errors: A Bayesian approach
Guillermo Ferreira;
Guillermo Ferreira
Department of Statistics,Universidad de Concepción,
Chile
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Mauricio Castro;
Mauricio Castro
Department of Statistics,Universidad de Concepción,
Chile
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Victor H. Lachos
Victor H. Lachos
Department of Statistics, Campinas State University,
Brazil
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AIP Conf. Proc. 1490, 116–125 (2012)
Citation
Guillermo Ferreira, Mauricio Castro, Victor H. Lachos; Partially linear models with autoregressive scale-mixtures of normal errors: A Bayesian approach. AIP Conf. Proc. 18 October 2012; 1490 (1): 116–125. https://doi.org/10.1063/1.4759595
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