估計單指標模型中單一解釋變數的主效應

Translated title of the contribution: Estimating the main effect of a covariate in single index models

Ming-Yen Cheng, Yu-Teng Shen

Research output: Contribution to journalArticlepeer-review

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 contributionEstimating the main effect of a covariate in single index models
Original languageChinese (Traditional)
Pages (from-to)272-313
Number of pages41
JournalJournal of the Chinese Statistical Association
Volume47
Issue number4
DOIs
Publication statusPublished - 1 Dec 2009

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