Empirical likelihood for quantile regression models with response data missing at random
This paper studies quantile linear regression models with response data missing at random. A quantile empirical-likelihood-based method is proposed firstly to study a quantile linear regression model with response data missing at random. It follows that a class of quantile empirical log-likelihood r...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2017-03-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2017-0028 |
| _version_ | 1818358411391139840 |
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| author | Luo S. Pang Shuxia |
| author_facet | Luo S. Pang Shuxia |
| author_sort | Luo S. |
| collection | DOAJ |
| description | This paper studies quantile linear regression models with response data missing at random. A quantile empirical-likelihood-based method is proposed firstly to study a quantile linear regression model with response data missing at random. It follows that a class of quantile empirical log-likelihood ratios including quantile empirical likelihood ratio with complete-case data, weighted quantile empirical likelihood ratio and imputed quantile empirical likelihood ratio are defined for the regression parameters. Then, a bias-corrected quantile empirical log-likelihood ratio is constructed for the mean of the response variable for a given quantile level. It is proved that these quantile empirical log-likelihood ratios are asymptotically χ2 distribution. Furthermore, a class of estimators for the regression parameters and the mean of the response variable are constructed, and the asymptotic normality of the proposed estimators is established. Our results can be used directly to construct the confidence intervals (regions) of the regression parameters and the mean of the response variable. Finally, simulation studies are conducted to assess the finite sample performance and a real-world data set is analyzed to illustrate the applications of the proposed method. |
| first_indexed | 2024-12-13T20:28:34Z |
| format | Article |
| id | doaj.art-6b834bfa83b2443389a37cd3be6d8351 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-13T20:28:34Z |
| publishDate | 2017-03-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-6b834bfa83b2443389a37cd3be6d83512022-12-21T23:32:29ZengDe GruyterOpen Mathematics2391-54552017-03-0115131733010.1515/math-2017-0028math-2017-0028Empirical likelihood for quantile regression models with response data missing at randomLuo S.0Pang Shuxia1School of Science, Xi’an Polytechnic University, Xi’an, Shaanxi 710048, ChinaSchool of Computer and Communication, Lanzhou University of Technology, Lanzhou, Gansu, 730000, ChinaThis paper studies quantile linear regression models with response data missing at random. A quantile empirical-likelihood-based method is proposed firstly to study a quantile linear regression model with response data missing at random. It follows that a class of quantile empirical log-likelihood ratios including quantile empirical likelihood ratio with complete-case data, weighted quantile empirical likelihood ratio and imputed quantile empirical likelihood ratio are defined for the regression parameters. Then, a bias-corrected quantile empirical log-likelihood ratio is constructed for the mean of the response variable for a given quantile level. It is proved that these quantile empirical log-likelihood ratios are asymptotically χ2 distribution. Furthermore, a class of estimators for the regression parameters and the mean of the response variable are constructed, and the asymptotic normality of the proposed estimators is established. Our results can be used directly to construct the confidence intervals (regions) of the regression parameters and the mean of the response variable. Finally, simulation studies are conducted to assess the finite sample performance and a real-world data set is analyzed to illustrate the applications of the proposed method.https://doi.org/10.1515/math-2017-0028quantile regressionempirical likelihoodmissing response dataconfidence interval62g0562g2060g42 |
| spellingShingle | Luo S. Pang Shuxia Empirical likelihood for quantile regression models with response data missing at random Open Mathematics quantile regression empirical likelihood missing response data confidence interval 62g05 62g20 60g42 |
| title | Empirical likelihood for quantile regression models with response data missing at random |
| title_full | Empirical likelihood for quantile regression models with response data missing at random |
| title_fullStr | Empirical likelihood for quantile regression models with response data missing at random |
| title_full_unstemmed | Empirical likelihood for quantile regression models with response data missing at random |
| title_short | Empirical likelihood for quantile regression models with response data missing at random |
| title_sort | empirical likelihood for quantile regression models with response data missing at random |
| topic | quantile regression empirical likelihood missing response data confidence interval 62g05 62g20 60g42 |
| url | https://doi.org/10.1515/math-2017-0028 |
| work_keys_str_mv | AT luos empiricallikelihoodforquantileregressionmodelswithresponsedatamissingatrandom AT pangshuxia empiricallikelihoodforquantileregressionmodelswithresponsedatamissingatrandom |