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題 名 | Model Indexing and Smoothing Parameter Selection in Nonparametric Function Estimation |
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作 者 | Gu,Chong; | 書刊名 | Statistica Sinica |
卷 期 | 8:3 1998.07[民87.07] |
頁 次 | 頁607-646 |
分類號 | 319.5 |
關鍵詞 | 無母數函數估計; 核方法; 負相關; Constraint; Cross-validation; Kernel method; Negative correlation; Penalized likelihood; Plug-in method; |
語 文 | 英文(English) |
英文摘要 | Smoothing parameter selection is among the most intensively studied subjects in nonparametric function estimation. A closely related issue, that of identifying a proper index for the smoothing parameter, is however largely neglected in the existing literature. Through heuristic arguments and simple simulations, we show that most current working indices are conceptually “incorrect”, in the sense that they are not interpretable across-replicate in repeated experiments. As a consequence, a few popular working concepts, such as expected mean square error and “degrees of freedom”, appear vulnerable under close scrutiny. Due to technical constraints, the arguments are mainly developed in the penalized likelihood setting, but conceptual parallels can be drawn to other settings as well as. In the light of our findings, simulations and discussion are also presented to compare the relative merits of the simple cross-validation method versus the more sophisticated plug-in method for smoothing parameter selection, and to explore related issues. The development stems fro man attempt to understand the well-publicized negative correlation between optimal and cross-validation smoothing parameters, which however turns out to bear little statistical relevance. |
本系統中英文摘要資訊取自各篇刊載內容。