Heavy-Tailed NGG Mixture Models
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866913773360513024 |
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| author | Ramirez, Vianey Palacios de Carvalho, Miguel Inostroza, Luis Gutierrez |
| author_facet | Ramirez, Vianey Palacios de Carvalho, Miguel Inostroza, Luis Gutierrez |
| contents | Heavy tails are often found in practice, and yet they are an Achilles heel of a variety of mainstream random probability measures such as the Dirichlet process (DP). The first contribution of this paper focuses on characterizing the tails of the so-called normalized generalized gamma (NGG) process. We show that the right tail of an NGG process is heavy-tailed provided that the centering distribution is itself heavy-tailed; the DP is the only member of the NGG class that fails to obey this convenient property. A second contribution of the paper rests on the development of two classes of heavy-tailed mixture models and the assessment of their relative merits. Multivariate extensions of the proposed heavy-tailed mixtures are devised here, along with a predictor-dependent version, to learn about the effect of covariates on a multivariate heavy-tailed response. The simulation study suggests that the proposed method performs well in various scenarios, and we showcase the application of the proposed methods in a neuroscience dataset. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_00867 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Heavy-Tailed NGG Mixture Models Ramirez, Vianey Palacios de Carvalho, Miguel Inostroza, Luis Gutierrez Statistics Theory Heavy tails are often found in practice, and yet they are an Achilles heel of a variety of mainstream random probability measures such as the Dirichlet process (DP). The first contribution of this paper focuses on characterizing the tails of the so-called normalized generalized gamma (NGG) process. We show that the right tail of an NGG process is heavy-tailed provided that the centering distribution is itself heavy-tailed; the DP is the only member of the NGG class that fails to obey this convenient property. A second contribution of the paper rests on the development of two classes of heavy-tailed mixture models and the assessment of their relative merits. Multivariate extensions of the proposed heavy-tailed mixtures are devised here, along with a predictor-dependent version, to learn about the effect of covariates on a multivariate heavy-tailed response. The simulation study suggests that the proposed method performs well in various scenarios, and we showcase the application of the proposed methods in a neuroscience dataset. |
| title | Heavy-Tailed NGG Mixture Models |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2211.00867 |