鄭明燕臺灣大學：數學研究所沈愈騰Shen, Yu-TengYu-TengShen2007-11-282018-06-282007-11-282018-06-282007http://ntur.lib.ntu.edu.tw//handle/246246/59472The 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。目錄: 中文摘要 i 英文摘要 ii 謝辭 iii 1. 導論 1 2 .Case I 的討論 4 3.估計 5 3.1 如何估計ai? 5 3.2 如何估計 E[cos(iπZ/2)] 和 E[sin(iπZ/2)]? 6 3.3 如何估計 h(x,z)? 6 4. Case II 的討論 8 5. 模擬結果 10 參考文獻 29597897 bytesapplication/pdfen-US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。Denoised scattergramNonparametric regressionAuxiliary covariatesSingle index modelAsymptotic sharp minimax estimate.thesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/59472/1/ntu-96-R94221038-1.pdf