Bayesian quantile regression for single-index models
Using an asymmetric Laplace distribution, which provides a mechanism for Bayesian inference of quantile regression models, we develop a fully Bayesian approach to fitting single-index models in conditional quantile regression. In this work, we use a Gaussian process prior for the unknown nonparametr...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2013
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| Online Access: | https://hdl.handle.net/10356/99409 http://hdl.handle.net/10220/17383 |
| _version_ | 1811678826311188480 |
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| author | Hu, Yuao Lian, Heng Gramacy, Robert B. |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Hu, Yuao Lian, Heng Gramacy, Robert B. |
| author_sort | Hu, Yuao |
| collection | NTU |
| description | Using an asymmetric Laplace distribution, which provides a mechanism for Bayesian inference of quantile regression models, we develop a fully Bayesian approach to fitting single-index models in conditional quantile regression. In this work, we use a Gaussian process prior for the unknown nonparametric link function and a Laplace distribution on the index vector, with the latter motivated by the recent popularity of the Bayesian lasso idea. We design a Markov chain Monte Carlo algorithm for posterior inference. Careful consideration of the singularity of the kernel matrix, and tractability of some of the full conditional distributions leads to a partially collapsed approach where the nonparametric link function is integrated out in some of the sampling steps. Our simulations demonstrate the superior performance of the Bayesian method versus the frequentist approach. The method is further illustrated by an application to the hurricane data. |
| first_indexed | 2024-10-01T02:59:26Z |
| format | Journal Article |
| id | ntu-10356/99409 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T02:59:26Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | ntu-10356/994092020-03-07T12:37:22Z Bayesian quantile regression for single-index models Hu, Yuao Lian, Heng Gramacy, Robert B. School of Physical and Mathematical Sciences Using an asymmetric Laplace distribution, which provides a mechanism for Bayesian inference of quantile regression models, we develop a fully Bayesian approach to fitting single-index models in conditional quantile regression. In this work, we use a Gaussian process prior for the unknown nonparametric link function and a Laplace distribution on the index vector, with the latter motivated by the recent popularity of the Bayesian lasso idea. We design a Markov chain Monte Carlo algorithm for posterior inference. Careful consideration of the singularity of the kernel matrix, and tractability of some of the full conditional distributions leads to a partially collapsed approach where the nonparametric link function is integrated out in some of the sampling steps. Our simulations demonstrate the superior performance of the Bayesian method versus the frequentist approach. The method is further illustrated by an application to the hurricane data. 2013-11-07T06:52:23Z 2019-12-06T20:06:54Z 2013-11-07T06:52:23Z 2019-12-06T20:06:54Z 2012 2012 Journal Article Hu, Y., Gramacy, R. B., & Lian, H. (2013). Bayesian quantile regression for single-index models. Statistics and Computing, 23(4), 437-454. https://hdl.handle.net/10356/99409 http://hdl.handle.net/10220/17383 10.1007/s11222-012-9321-0 en Statistics and computing |
| spellingShingle | Hu, Yuao Lian, Heng Gramacy, Robert B. Bayesian quantile regression for single-index models |
| title | Bayesian quantile regression for single-index models |
| title_full | Bayesian quantile regression for single-index models |
| title_fullStr | Bayesian quantile regression for single-index models |
| title_full_unstemmed | Bayesian quantile regression for single-index models |
| title_short | Bayesian quantile regression for single-index models |
| title_sort | bayesian quantile regression for single index models |
| url | https://hdl.handle.net/10356/99409 http://hdl.handle.net/10220/17383 |
| work_keys_str_mv | AT huyuao bayesianquantileregressionforsingleindexmodels AT lianheng bayesianquantileregressionforsingleindexmodels AT gramacyrobertb bayesianquantileregressionforsingleindexmodels |