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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.17987 |
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| _version_ | 1866917579684052992 |
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| author | Barreiro-Ures, Daniel Cao, Ricardo Fernández, Mario Francisco Hart, Jeffrey D. |
| author_facet | Barreiro-Ures, Daniel Cao, Ricardo Fernández, Mario Francisco Hart, Jeffrey D. |
| contents | Hall and Robinson (2009) proposed and analyzed the use of bagged cross-validation to choose the bandwidth of a kernel density estimator. They established that bagging greatly reduces the noise inherent in ordinary cross-validation, and hence leads to a more efficient bandwidth selector. The asymptotic theory of Hall and Robinson (2009) assumes that $N$, the number of bagged subsamples, is $\infty$. We expand upon their theoretical results by allowing $N$ to be finite, as it is in practice. Our results indicate an important difference in the rate of convergence of the bagged cross-validation bandwidth for the cases $N=\infty$ and $N<\infty$. Simulations quantify the improvement in statistical efficiency and computational speed that can result from using bagged cross-validation as opposed to a binned implementation of ordinary cross-validation. The performance of thebagged bandwidth is also illustrated on a real, very large, data set. Finally, a byproduct of our study is the correction of errors appearing in the Hall and Robinson (2009) expression for the asymptotic mean squared error of the bagging selector. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17987 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bagging cross-validated bandwidths with application to Big Data Barreiro-Ures, Daniel Cao, Ricardo Fernández, Mario Francisco Hart, Jeffrey D. Methodology 62G07 (Primary), 62G20 (Secondary) Hall and Robinson (2009) proposed and analyzed the use of bagged cross-validation to choose the bandwidth of a kernel density estimator. They established that bagging greatly reduces the noise inherent in ordinary cross-validation, and hence leads to a more efficient bandwidth selector. The asymptotic theory of Hall and Robinson (2009) assumes that $N$, the number of bagged subsamples, is $\infty$. We expand upon their theoretical results by allowing $N$ to be finite, as it is in practice. Our results indicate an important difference in the rate of convergence of the bagged cross-validation bandwidth for the cases $N=\infty$ and $N<\infty$. Simulations quantify the improvement in statistical efficiency and computational speed that can result from using bagged cross-validation as opposed to a binned implementation of ordinary cross-validation. The performance of thebagged bandwidth is also illustrated on a real, very large, data set. Finally, a byproduct of our study is the correction of errors appearing in the Hall and Robinson (2009) expression for the asymptotic mean squared error of the bagging selector. |
| title | Bagging cross-validated bandwidths with application to Big Data |
| topic | Methodology 62G07 (Primary), 62G20 (Secondary) |
| url | https://arxiv.org/abs/2401.17987 |