Jackknife Empirical Likelihood Inference for the Variance Residual Life Function
In life testing situations, the residual life time of a component which has survived t units of time is Xt = X −t|X > t. In this paper, we give a central limit theorem result for the estimator of Var(Xt), the variance residual life(VRL) function. The result is used to construct normal approximat...
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| Format: | Article |
| Language: | English |
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Instituto Nacional de Estatística | Statistics Portugal
2021-03-01
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| Series: | Revstat Statistical Journal |
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| Online Access: | https://revstat.ine.pt/index.php/REVSTAT/article/view/329 |
| _version_ | 1818513220969693184 |
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| author | Vali Zardasht |
| author_facet | Vali Zardasht |
| author_sort | Vali Zardasht |
| collection | DOAJ |
| description |
In life testing situations, the residual life time of a component which has survived t units of time is Xt = X −t|X > t. In this paper, we give a central limit theorem result for the estimator of Var(Xt), the variance residual life(VRL) function. The result is used to construct normal approximation based confidence interval for the VRL. Furthermore, we use the jackknife empirical likelihood ratio procedure to obtain confidence interval for the VRL function. These intervals are compared through simulation study in terms of the average length and coverage probability. Finally, a numerical example illustrating the theory is also given.
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| first_indexed | 2024-12-10T23:58:13Z |
| format | Article |
| id | doaj.art-464b9bc307cf40b3afc5d3442f6da3c9 |
| institution | Directory Open Access Journal |
| issn | 1645-6726 2183-0371 |
| language | English |
| last_indexed | 2024-12-10T23:58:13Z |
| publishDate | 2021-03-01 |
| publisher | Instituto Nacional de Estatística | Statistics Portugal |
| record_format | Article |
| series | Revstat Statistical Journal |
| spelling | doaj.art-464b9bc307cf40b3afc5d3442f6da3c92022-12-22T01:28:32ZengInstituto Nacional de Estatística | Statistics PortugalRevstat Statistical Journal1645-67262183-03712021-03-0119110.57805/revstat.v19i1.329Jackknife Empirical Likelihood Inference for the Variance Residual Life FunctionVali Zardasht 0University of Mohaghegh Ardabili In life testing situations, the residual life time of a component which has survived t units of time is Xt = X −t|X > t. In this paper, we give a central limit theorem result for the estimator of Var(Xt), the variance residual life(VRL) function. The result is used to construct normal approximation based confidence interval for the VRL. Furthermore, we use the jackknife empirical likelihood ratio procedure to obtain confidence interval for the VRL function. These intervals are compared through simulation study in terms of the average length and coverage probability. Finally, a numerical example illustrating the theory is also given. https://revstat.ine.pt/index.php/REVSTAT/article/view/329confidence intervalcoverage probabilityjackknife empirical likelihoodU-statistic |
| spellingShingle | Vali Zardasht Jackknife Empirical Likelihood Inference for the Variance Residual Life Function Revstat Statistical Journal confidence interval coverage probability jackknife empirical likelihood U-statistic |
| title | Jackknife Empirical Likelihood Inference for the Variance Residual Life Function |
| title_full | Jackknife Empirical Likelihood Inference for the Variance Residual Life Function |
| title_fullStr | Jackknife Empirical Likelihood Inference for the Variance Residual Life Function |
| title_full_unstemmed | Jackknife Empirical Likelihood Inference for the Variance Residual Life Function |
| title_short | Jackknife Empirical Likelihood Inference for the Variance Residual Life Function |
| title_sort | jackknife empirical likelihood inference for the variance residual life function |
| topic | confidence interval coverage probability jackknife empirical likelihood U-statistic |
| url | https://revstat.ine.pt/index.php/REVSTAT/article/view/329 |
| work_keys_str_mv | AT valizardasht jackknifeempiricallikelihoodinferenceforthevarianceresiduallifefunction |