Bayesian diagnostics in a partially linear model with first-order autoregressive skew-normal errors
This paper studies a Bayesian local influence method to detect influential observations in a partially linear model with first-order autoregressive skew-normal errors. This method appears suitable for small or moderate-sized data sets (n=200∼400) and overcomes some theoretical limitations, bridging...
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| Published in | Computational statistics Vol. 40; no. 2; pp. 1021 - 1051 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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Heidelberg
Springer Nature B.V
01.02.2025
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| Online Access | Get full text |
| ISSN | 0943-4062 1613-9658 |
| DOI | 10.1007/s00180-024-01504-2 |
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| Abstract | This paper studies a Bayesian local influence method to detect influential observations in a partially linear model with first-order autoregressive skew-normal errors. This method appears suitable for small or moderate-sized data sets (n=200∼400) and overcomes some theoretical limitations, bridging the diagnostic gap for small or moderate-sized data in classical methods. The MCMC algorithm is employed for parameter estimation, and Bayesian local influence analysis is made using three perturbation schemes (priors, variances, and data) and three measurement scales (Bayes factor, ϕ-divergence, and posterior mean). Simulation studies are conducted to validate the reliability of the diagnostics. Finally, a practical application uses data on the 1976 Los Angeles ozone concentration to further demonstrate the effectiveness of the diagnostics. |
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| AbstractList | This paper studies a Bayesian local influence method to detect influential observations in a partially linear model with first-order autoregressive skew-normal errors. This method appears suitable for small or moderate-sized data sets (n=200∼400) and overcomes some theoretical limitations, bridging the diagnostic gap for small or moderate-sized data in classical methods. The MCMC algorithm is employed for parameter estimation, and Bayesian local influence analysis is made using three perturbation schemes (priors, variances, and data) and three measurement scales (Bayes factor, ϕ-divergence, and posterior mean). Simulation studies are conducted to validate the reliability of the diagnostics. Finally, a practical application uses data on the 1976 Los Angeles ozone concentration to further demonstrate the effectiveness of the diagnostics. |
| Author | Liu, Shuangzhe Paula, Gilberto A. Lu, Jiawei Liu, Yonghui |
| Author_xml | – sequence: 1 givenname: Yonghui surname: Liu fullname: Liu, Yonghui – sequence: 2 givenname: Jiawei surname: Lu fullname: Lu, Jiawei – sequence: 3 givenname: Gilberto A. surname: Paula fullname: Paula, Gilberto A. – sequence: 4 givenname: Shuangzhe orcidid: 0000-0002-4858-2789 surname: Liu fullname: Liu, Shuangzhe |
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| References | S Liu (1504_CR17) 2000; 41 RD Cook (1504_CR4) 1986; 48 HX Hao (1504_CR14) 2019; 4 YH Liu (1504_CR20) 2020; 8 H Zhu (1504_CR36) 2001; 63 A Azzalini (1504_CR2) 1985; 12 C Crainiceanu (1504_CR5) 2005; 14 YH Liu (1504_CR22) 2024; 51 XW Dai (1504_CR6) 2019; 60 J Marriott (1504_CR25) 1998; 66 YH Liu (1504_CR23) 2023; 93 YY Ju (1504_CR15) 2022; 10 G Ferreira (1504_CR11) 2013; 8 N Tang (1504_CR33) 2014; 126 J Albert (1504_CR1) 2007 YH Liu (1504_CR24) 2022 SY Lee (1504_CR16) 2004; 45 RA Oliveira (1504_CR26) 2021; 36 H Zhu (1504_CR35) 2011; 98 S Sturtz (1504_CR32) 2005; 12 GA Paula (1504_CR27) 2012; 28 S Zeger (1504_CR34) 1994; 50 F Dominici (1504_CR7) 2004; 9 D Ruppert (1504_CR29) 2003 CS Ferreira (1504_CR10) 2022; 37 YH Liu (1504_CR21) 2017; 71 CS Ferreira (1504_CR8) 2022; 36 MP Galea (1504_CR12) 1997; 46 WY Poon (1504_CR28) 1999; 61 GAF Seber (1504_CR31) 1989 1504_CR13 SK Sahu (1504_CR30) 2003; 31 CA Cardozo (1504_CR3) 2022; 63 S Liu (1504_CR19) 2022; 188 S Liu (1504_CR18) 2004; 41A CS Ferreira (1504_CR9) 2017; 44 |
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| Title | Bayesian diagnostics in a partially linear model with first-order autoregressive skew-normal errors |
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