Jackknife Empirical Likelihood Method for U Statistics Based on Multivariate Samples and its Applications
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866918226248597504 |
|---|---|
| author | Garg, Naresh Mathew, Litty Dewan, Isha Kattumannil, Sudheesh Kumar |
| author_facet | Garg, Naresh Mathew, Litty Dewan, Isha Kattumannil, Sudheesh Kumar |
| contents | We develop a jackknife empirical likelihood (JEL) framework for inference on parameters defined through multivariate three-sample U-statistic. From three independent multivariate samples, we construct JEL ratio statistic based on suitable jackknife pseudo-values and, under mild regularity conditions, establish a Wilks-type result showing that the log JEL ratio converges in distribution to a chi-square limit. This provides asymptotically valid confidence intervals for the parameter of interest without explicit variance estimation or heavy resampling. To illustrate the usefulness of the proposed method, we construct confidence intervals for differences in volume under the surface (VUS) measures, which are widely used in classification problems. Through Monte Carlo simulations, we compare the performance of JEL-based confidence intervals with those obtained from normal approximation of U-statistic and kernel-based methods. The findings indicate that the proposed JEL approach outperforms existing methods in terms of coverage probability and computational efficiency. Finally, we apply our methods to a recent real dataset. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14038 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Jackknife Empirical Likelihood Method for U Statistics Based on Multivariate Samples and its Applications Garg, Naresh Mathew, Litty Dewan, Isha Kattumannil, Sudheesh Kumar Methodology Statistics Theory We develop a jackknife empirical likelihood (JEL) framework for inference on parameters defined through multivariate three-sample U-statistic. From three independent multivariate samples, we construct JEL ratio statistic based on suitable jackknife pseudo-values and, under mild regularity conditions, establish a Wilks-type result showing that the log JEL ratio converges in distribution to a chi-square limit. This provides asymptotically valid confidence intervals for the parameter of interest without explicit variance estimation or heavy resampling. To illustrate the usefulness of the proposed method, we construct confidence intervals for differences in volume under the surface (VUS) measures, which are widely used in classification problems. Through Monte Carlo simulations, we compare the performance of JEL-based confidence intervals with those obtained from normal approximation of U-statistic and kernel-based methods. The findings indicate that the proposed JEL approach outperforms existing methods in terms of coverage probability and computational efficiency. Finally, we apply our methods to a recent real dataset. |
| title | Jackknife Empirical Likelihood Method for U Statistics Based on Multivariate Samples and its Applications |
| topic | Methodology Statistics Theory |
| url | https://arxiv.org/abs/2408.14038 |