图 书 馆
在功能回归预测误差The prediction error in functional regression |
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| 课程网址: | http://videolectures.net/sip08_kneip_tpeifr/ |
| 主讲教师: | Alois Kneip |
| 开课单位: | 波恩大学 |
| 开课时间: | 2008-12-18 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | The talk considers functional linear regression, where scalar responses Y are modeled in dependence of random functions. We propose a smoothing splines estimator for the functional slope parameter based on a slight modi- fication of the usual penalty. Theoretical analysis concentrates on the error in an out-of-sample prediction of the response for a new random function. It is shown that rates of convergence of the prediction error depend on the smoothness of the slope function and on the structure of the predictors. We then prove that these rates are optimal in the sense that they are minimax over large classes of possible slope functions and distributions of the predic- tive curves. For the case of models with errors-in-variables the smoothing spline estimator is modified by using a denoising correction of the covari- ance matrix of discretized curves. The methodology is then applied to a real case study where the aim is to predict the maximum of the concentration of ozone by using the curve of this concentration measured the preceding day. |
| 关 键 词: | 线性回归; 随机函数; 斜坡函数 |
| 课程来源: | 视频讲座网 |
| 最后编审: | 2020-06-29：wuyq |
| 阅读次数: | 180 |