Empirical likelihood confidence regions of the parameters in a partially single-index varying-coefficient model
In this paper, we investigate a partially single-index varying-coefficient model, and suggest two empirical log-likelihood ratio statistics for the unknown parameters in the model. The first statistic is asymptotically distributed as a weighted sum of independent chi-square variables under some mild...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2019-07-01
|
| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2019-0059 |
| _version_ | 1819114964668907520 |
|---|---|
| author | Xiang Xing Liu Wanrong |
| author_facet | Xiang Xing Liu Wanrong |
| author_sort | Xiang Xing |
| collection | DOAJ |
| description | In this paper, we investigate a partially single-index varying-coefficient model, and suggest two empirical log-likelihood ratio statistics for the unknown parameters in the model. The first statistic is asymptotically distributed as a weighted sum of independent chi-square variables under some mild conditions. It is proved that another statistic, with adjustment factor, is asymptotically standard chi-square under some suitable conditions. These useful statistics could be used to construct the confidence regions of the parameters. A simulation study indicates that, with the increase of sample size, the coverage probability of the confidence region constructed by us gradually approaches the theoretical value. |
| first_indexed | 2024-12-22T04:53:40Z |
| format | Article |
| id | doaj.art-2ae5641327b245548c2fb3321ae323e9 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-22T04:53:40Z |
| publishDate | 2019-07-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-2ae5641327b245548c2fb3321ae323e92022-12-21T18:38:26ZengDe GruyterOpen Mathematics2391-54552019-07-0117172874110.1515/math-2019-0059math-2019-0059Empirical likelihood confidence regions of the parameters in a partially single-index varying-coefficient modelXiang Xing0Liu Wanrong1Hunan Normal University Changsha, Changsha, ChinaHunan Normal University Changsha, Changsha, ChinaIn this paper, we investigate a partially single-index varying-coefficient model, and suggest two empirical log-likelihood ratio statistics for the unknown parameters in the model. The first statistic is asymptotically distributed as a weighted sum of independent chi-square variables under some mild conditions. It is proved that another statistic, with adjustment factor, is asymptotically standard chi-square under some suitable conditions. These useful statistics could be used to construct the confidence regions of the parameters. A simulation study indicates that, with the increase of sample size, the coverage probability of the confidence region constructed by us gradually approaches the theoretical value.https://doi.org/10.1515/math-2019-0059confidence regionempirical likelihoodpartially single-index varying-coefficient modelchi-square distribution62-xx |
| spellingShingle | Xiang Xing Liu Wanrong Empirical likelihood confidence regions of the parameters in a partially single-index varying-coefficient model Open Mathematics confidence region empirical likelihood partially single-index varying-coefficient model chi-square distribution 62-xx |
| title | Empirical likelihood confidence regions of the parameters in a partially single-index varying-coefficient model |
| title_full | Empirical likelihood confidence regions of the parameters in a partially single-index varying-coefficient model |
| title_fullStr | Empirical likelihood confidence regions of the parameters in a partially single-index varying-coefficient model |
| title_full_unstemmed | Empirical likelihood confidence regions of the parameters in a partially single-index varying-coefficient model |
| title_short | Empirical likelihood confidence regions of the parameters in a partially single-index varying-coefficient model |
| title_sort | empirical likelihood confidence regions of the parameters in a partially single index varying coefficient model |
| topic | confidence region empirical likelihood partially single-index varying-coefficient model chi-square distribution 62-xx |
| url | https://doi.org/10.1515/math-2019-0059 |
| work_keys_str_mv | AT xiangxing empiricallikelihoodconfidenceregionsoftheparametersinapartiallysingleindexvaryingcoefficientmodel AT liuwanrong empiricallikelihoodconfidenceregionsoftheparametersinapartiallysingleindexvaryingcoefficientmodel |