估計單指標模型中單一解釋變數的主效應

Estimating the main effect of a covariate in single-index models

沈愈騰(Yu-Teng Shen)

指導教授 ： 鄭明燕

國立臺灣大學/理學院/數學研究所/碩士(2007年)

https://doi.org/10.6342/NTU.2007.03061

摘要

無資料

關鍵字

降噪散點圖 ； 無母數迴歸 ； 輔助變數 ； 單指標模型 ； 概略尖銳極小化最大值估計。

並列摘要

The article Efromovich (2005) addresses the problem of finding a relationship between the univariate predictor and the response when regression errors, created in part by known auxiliary covariates, are too large for a reliable regression estimation. The proposed solution of Efromovich (2005) is to estimate the noise component
h(x,z) and substract it from the response and the obtained denoise scattergram yields the optimal estimation of the regression function. Besides, Efromovich (2005) develops a theory of asymptotically optimal nonparametric univariate regression estimation in the presence of auxiliary covariates. This article discusses the problem under single index model. The problem is to estimate
the main effect of a covariate in single-index models. I estimate h(x,z) and substract it from the response and prove the obtained denoise scattergram yields
an asymptotic sharp minimax estimate。

並列關鍵字

Denoised scattergram ； Nonparametric regression ； Auxiliary covariates ； Single index model ； Asymptotic sharp minimax estimate.

參考文獻

Efromovich,S. (2005). Univariate nonparametric regression in the presence of auxiliary covariates.

Journal of the American Statistical Association,100,1185-1201.

Nonparametric Regression, 'Statistica Sinica, 6,925-945.

Efromovich,S. (1999). Nonparametric Curve Estimation: Methods, Theory and Applications, New York: Springer-Verlag.

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