Assessing prediction error of nonparametric regression and classification under Bregman divergence
| dc.creator | Fan, Jianqing | |
| dc.creator | Zhang, Chunming | |
| dc.date | 2005-06-02 | |
| dc.date.accessioned | 2026-07-07T08:06:58Z | |
| dc.date.available | 2026-07-07T08:06:58Z | |
| dc.description | Prediction error is critical to assessing the performance of statistical methods and selecting statistical models. We propose the cross-validation and approximated cross-validation methods for estimating prediction error under a broad q-class of Bregman divergence for error measures which embeds nearly all of the commonly used loss functions in regression, classification procedures and machine learning literature. The approximated cross-validation formulas are analytically derived, which facilitate fast estimation of prediction error under the Bregman divergence. We then study a data-driven optimal bandwidth selector for the local-likelihood estimation that minimizes the overall prediction error or equivalently the covariance penalty. It is shown that the covariance penalty and cross-validation methods converge to the same mean-prediction-error-criterion. We also propose a lower-bound scheme for computing the local logistic regression estimates and demonstrate that it is as simple and stable as the local least-squares regression estimation. The algorithm monotonically enhances the target local-likelihood and converges. The idea and methods are extended to the generalized varying-coefficient models and semiparametric models. | |
| dc.description | 38 pages, 8 figures | |
| dc.identifier | https://arxiv.org/abs/math/0506028 | |
| dc.identifier | http://arxiv.org/abs/math/0506028 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130787 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62G05 62H30 | |
| dc.title | Assessing prediction error of nonparametric regression and classification under Bregman divergence | |
| dc.type | text |