Abstract
Efromovich (2005)提出利用輔助變數估計一元無母數迴歸的方法，並委展出在輔助變數存在時無母數迴歸的漸進最佳預利(asymptotically optimal nonparametric univariate regression estimation in the presence of auxiliary covariate)的定理。Efromovich(2005)先估計h(X,Z)=E(Y|X,Z)-e(Y|X)然後用Y扣掉它，產生峰噪散點圖(denoised scattergram)，以此來估計E(Y|X=x)，這裡Z是一個輔助變數。本篇論文討論在單指標模型中，如何估計單一解釋變數的主效應，我們以Efromovich (2005)文章中的方法爲基礎，對h(x, z)重新估計，產生降噪散點圖(denoised scattergram)來估計f(x)=E(Y|X=x),並證明此估計也是一個漸進尖銳極小化最大值估計(asymptotic sharp minimax estimate)。
| Translated title of the contribution | Estimating the main effect of a covariate in single index models |
|---|---|
| Original language | Chinese (Traditional) |
| Pages (from-to) | 272-313 |
| Number of pages | 41 |
| Journal | Journal of the Chinese Statistical Association |
| Volume | 47 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 1 Dec 2009 |