具不連續性平滑曲面之估計

Abstract

本篇論文主要是根據 Shiau(1985) 中對於具不連續性高維度函數的兩個 估計方法以 模擬方式來探討其可行性同時我們利用廣義的交叉確認準 則(generalized cross valida tion)簡稱 GCV ,來選取適當的平滑參 數(smoothing parameter),並且,我們用均方誤差(m ean square error) 來確認 GCV 方法的可靠性.模擬的結果顯示, Shiau(1985) 提出的方 法,在我們所使用的測試函數的估計上均有不錯的表現.而且當干擾( noisy)很大時整個函 數的形狀亦可表現出來. In this work, we investigate emprically the validity of the methodologies develoed in Shiau (1985) for estimating a multivariate function with disconti- nuities. Both the general case and special case are included in the study. For the choice of smoothing parameter λ, the generalized cross validation method is used. Further the mean squared error is also used for checking the validati ty of the GCV. Our simulation results show that the methodologies proposed byS hiau(1985) are very promising and the functions are well recorved from noisy d ata.