頁籤選單縮合
題 名 | Surface Estimation, Variable Selection, and the Nonparametric Oracle Property |
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作 者 | Storlie, Curtis B.; Bondell, Howard D.; Reich, Brian J.; Zhang, Hao Helen; | 書刊名 | Statistica Sinica |
卷 期 | 21:2 2011.04[民100.04] |
頁 次 | 頁679-705 |
分類號 | 319.5 |
關鍵詞 | Adaptive LASSO; Nonparametric regression; Regularization method; Smoothing spline ANOVA; Variable selection; |
語 文 | 英文(English) |
英文摘要 | Abstract: Variable selection for multivariate nonparametric regression is an important, yet challenging, problem due, in part, to the infinite dimensionality of the function space. An ideal selection procedure would be automatic, stable, easy to use, and have desirable asymptotic properties. In particular, we define a selection procedure to be nonparametric oracle (np-oracle) if it consistently selects the correct subset of predictors and, at the same time, estimates the smooth surface at the optimal nonparametric rate, as the sample size goes to infinity. In this paper, we propose a model selection procedure for nonparametric models, and explore the conditions under which the new method enjoys the aforementioned properties. Developed in the framework of smoothing spline ANOVA, our estimator is obtained via solving a regularization problem with a novel adaptive penalty on the sum of functional component norms. Theoretical properties of the new estimator are established. Additionally, numerous simulations and examples suggest that the new approach substantially outperforms other existing methods in the finite sample setting. |
本系統中英文摘要資訊取自各篇刊載內容。