The DOI matches its Crossref record; 17 of the 17 references it cites were found in a registry or an index.
On Bayesian Modeling of Fat Tails and Skewness
Abstract
We consider a Bayesian analysis of linear regression models that can account for skewed error distributions with fat tails. The latter two features are often observed characteristics of empirical datasets, and we formally incorporate them in the inferential process. A general procedure for introducing skewness into symmetric distributions is first proposed. Even though this allows for a great deal of flexibility in distributional shape, tail behavior is not affected. Applying this skewness procedure to a Student t distribution, we generate a “skewed Student” distribution, which displays both flexible tails and possible skewness, each entirely controlled by a separate scalar parameter. The linear regression model with a skewed Student error term is the main focus of the article. We first characterize existence of the posterior distribution and its moments, using standard improper priors and allowing for inference on skewness and tail parameters. For posterior inference with this model, we suggest a numerical procedure using Gibbs sampling. The latter proves very easy to implement and renders the analysis of quite challenging problems a practical possibility. Some examples illustrate the use of this model in empirical data analysis.
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Cites
Sampling-based approaches to calculating marginal densities
Gelfand, A. E., & Smith, A. F. M. (1990) · Journal of the American Statistical Association · doi:10.1080/01621459.1990.10476213 · Cited by 6,606
Robust Regression and Outlier Detection
Piepel, G. F. (1989) · Technometrics · doi:10.1080/00401706.1989.10488524 · Cited by 6,144
Robust Regression and Outlier Detection
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Non-Uniform Random Variate Generation
Devroye, L. (1986) · Springer eBooks · doi:10.1007/978-1-4613-8643-8 · Cited by 4,041
Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance: Stochastic Modeling
Samorodnitsky, G., & Taqqu, M. S. (2017) · Routledge eBooks · doi:10.1201/9780203738818 · Cited by 3,802
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Marginal Likelihood from the Gibbs Output
Chib, S. (1995) · Journal of the American Statistical Association · doi:10.1080/01621459.1995.10476635 · Cited by 1,905
Milner, R. (1976) · Cited by 742
Computing Bayes Factors Using a Generalization of the Savage-Dickey Density Ratio
Verdinelli, I., & Wasserman, L. (1995) · Journal of the American Statistical Association · doi:10.1080/01621459.1995.10476554 · Cited by 506
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The Skew-Normal and Related Families
Azzalini, A., & Capitanio, A. (2013) · Cambridge University Press eBooks · doi:10.1017/cbo9781139248891 · Cited by 710
A Skew Extension of the T-Distribution, with Applications
Jones, M. C., & Faddy, M. J. (2003) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/1467-9868.00378 · Cited by 326
Sharpening Wald-type inference in robust regression for small samples
Koller, M., & Stahel, W. A. (2011) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2011.02.014 · Cited by 286
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Metadata
- Authors
- Fernández, C., & Steel, M. F. J.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1998-03
- Volume
- 93
- Issue
- 441
- Pages
- 359-371
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W1639275303
- Cited by
- 1,083
- References
- 17
- FWCI
- 5.69
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
