鄭明燕2006-07-262018-06-282006-07-262018-06-282002-10-31http://ntur.lib.ntu.edu.tw//handle/246246/20957我們研究以非參數數方法估計被二維機率密度函數或具兩個解釋變數之迴歸函數 定義的曲面。我們建議一種有效減低變異量的估計方法。此方法可用於許多推論 問題如機率密度估計及迴歸，亦可用於許多型式的估計量。首先我們利用傳統的 曲面估計量建造一個估計曲面等高線的一次或二次曲線線段，建造方式乃使得傳 統的曲面估計量沿此線段有最小方差。有了此等高線估計線段，最終的曲面估計 值是所有沿著此線段一部份的傳統估計值的平均值。我們探討應用此方法至估計 機率密度函數曲面的核估計量。我們探討這些估計量的理論性質與數值表現。We suggest a method for reducing variance in nonparametric surface estimation. The technique is applicable to a wide range of inferential problems, including both density estimation and regression, and to a wide variety of estimator types. It is based on estimating the contours of a surface by minimizing deviations of of elementary surface estimates along a linear or quadratic curve. Once a contour estimate has been obtained, the final surface estimate is computed by averaging conventaional surface estimates along a portion of the contour. Theoretical and numerical properties of the technique are discussed.application/pdf115420 bytesapplication/pdfzh-TW國立臺灣大學數學系暨研究所帶寬值邊界效應核方法無母數機率密度估計無母數迴歸變異降低Bandwidthboundary effectkernel methodnonparametric density estimationnonparametric regressionvariance reductionreporthttp://ntur.lib.ntu.edu.tw/bitstream/246246/20957/1/902118M002011.pdf