Adaptive profile-empirical-likelihood inferences for generalized single-index models
We study generalized single-index models and propose an efficient equation for estimating the index parameter and unknown link function, deriving a quasi-likelihood-based maximum empirical likelihood estimator (QLMELE) of the index parameter. We then establish an efficient confidence region for any...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2013
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/96558 http://hdl.handle.net/10220/18078 |
| _version_ | 1826115856565796864 |
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| author | Huang, Zhensheng. Pang, Zhen. Zhang, Riquan. |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Huang, Zhensheng. Pang, Zhen. Zhang, Riquan. |
| author_sort | Huang, Zhensheng. |
| collection | NTU |
| description | We study generalized single-index models and propose an efficient equation for estimating the index parameter and unknown link function, deriving a quasi-likelihood-based maximum empirical likelihood estimator (QLMELE) of the index parameter. We then establish an efficient confidence region for any components of the index parameter using an adaptive empirical likelihood method. A pointwise confidence interval for the unknown link function is also established using the QLMELE. Compared with the normal approximation proposed by Cui et al. [Ann Stat. 39 (2011) 1658], our approach is more attractive not only theoretically but also empirically. Simulation studies demonstrate that the proposed method provides smaller confidence intervals than those based on the normal approximation method subject to the same coverage probabilities. Hence, the proposed empirical likelihood is preferable to the normal approximation method because of the complicated covariance estimation. An application to a real data set is also illustrated. |
| first_indexed | 2024-10-01T04:01:57Z |
| format | Journal Article |
| id | ntu-10356/96558 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T04:01:57Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | ntu-10356/965582020-03-07T12:34:42Z Adaptive profile-empirical-likelihood inferences for generalized single-index models Huang, Zhensheng. Pang, Zhen. Zhang, Riquan. School of Physical and Mathematical Sciences DRNTU::Science::Mathematics::Statistics We study generalized single-index models and propose an efficient equation for estimating the index parameter and unknown link function, deriving a quasi-likelihood-based maximum empirical likelihood estimator (QLMELE) of the index parameter. We then establish an efficient confidence region for any components of the index parameter using an adaptive empirical likelihood method. A pointwise confidence interval for the unknown link function is also established using the QLMELE. Compared with the normal approximation proposed by Cui et al. [Ann Stat. 39 (2011) 1658], our approach is more attractive not only theoretically but also empirically. Simulation studies demonstrate that the proposed method provides smaller confidence intervals than those based on the normal approximation method subject to the same coverage probabilities. Hence, the proposed empirical likelihood is preferable to the normal approximation method because of the complicated covariance estimation. An application to a real data set is also illustrated. 2013-12-05T03:25:13Z 2019-12-06T19:32:30Z 2013-12-05T03:25:13Z 2019-12-06T19:32:30Z 2013 2013 Journal Article Huang, Z., Pang, Z., & Zhang, R. (2013). Adaptive profile-empirical-likelihood inferences for generalized single-index models. Computational statistics & data analysis, 62, 70-82. 0167-9473 https://hdl.handle.net/10356/96558 http://hdl.handle.net/10220/18078 10.1016/j.csda.2012.12.006 en Computational statistics & data analysis |
| spellingShingle | DRNTU::Science::Mathematics::Statistics Huang, Zhensheng. Pang, Zhen. Zhang, Riquan. Adaptive profile-empirical-likelihood inferences for generalized single-index models |
| title | Adaptive profile-empirical-likelihood inferences for generalized single-index models |
| title_full | Adaptive profile-empirical-likelihood inferences for generalized single-index models |
| title_fullStr | Adaptive profile-empirical-likelihood inferences for generalized single-index models |
| title_full_unstemmed | Adaptive profile-empirical-likelihood inferences for generalized single-index models |
| title_short | Adaptive profile-empirical-likelihood inferences for generalized single-index models |
| title_sort | adaptive profile empirical likelihood inferences for generalized single index models |
| topic | DRNTU::Science::Mathematics::Statistics |
| url | https://hdl.handle.net/10356/96558 http://hdl.handle.net/10220/18078 |
| work_keys_str_mv | AT huangzhensheng adaptiveprofileempiricallikelihoodinferencesforgeneralizedsingleindexmodels AT pangzhen adaptiveprofileempiricallikelihoodinferencesforgeneralizedsingleindexmodels AT zhangriquan adaptiveprofileempiricallikelihoodinferencesforgeneralizedsingleindexmodels |