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題 名 | 傅立葉級數估式對一個迴歸函數的配適=The Fitting of A Regression Function Using the Fourier Series Estimator |
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作 者 | 林永立; 郭寶錚; 何兆銓; | 書刊名 | 農林學報 |
卷 期 | 48:3 1999.09[民88.09] |
頁 次 | 頁55-68 |
分類號 | 319.51 |
關鍵詞 | 傅立葉級數; 直交級數估式; 廣義交叉確認; 多項式的三角迴歸; Orthogonal series estimator; Fourier series; Generalized cross-validation; GCV; Polynomial-trigonometric regression; |
語 文 | 中文(Chinese) |
中文摘要 | 當觀測的資料具有週期性的現象時,可以考慮以包含正弦及餘弦的線性模式來估 計迴歸函數μ,典型傅立葉級數估式即為一例,但當迴歸函數無法滿足週期性的邊界條件時 , 利用誤差均方的方法來決定典型傅立葉級數估式中的三角函數項次多少的準則, 如 GVC 等,常會造成使用過多的項次,使得估式較為晃動。在典型傅立葉級數估式中如能加上低階 的多項式可解決無法滿足週期性邊界條件的問題,所得到的估式也較為平滑。本文將探討直 交級數估式的性質, 並以數例說明如何以 GCV 準則來選取典型傅立葉級數估式的項次,及 其求配過程和診斷分析等,並考慮加入低階多項式,以滿足邊界效應,並比較兩函數對資料 配適的表現。 |
英文摘要 | When the observed data exhibit periodic behavior, usually a linear model including sines and cosines is employed to estimate the regression function μ. The classical Fourier series estimator is of this type. However, if the regression function μ does not astisfy periodic boundary conditions, the criterion based on the mean squared error, i.e. GCV, to choose the number of trigonometric functions in the regression would yield too many terms and the chosen function performs wiggly. A combination of low-order polynomial and trigonometric terms culd alleviate the above problem and achieve a smooth curve. In this study, we tried to investigate the properties of orthogonal series estimator. A simulated data set was used to illustrate how to use GCV criteria to choose the number of trigonometric functions in this regression, the fitting, and diagnostic procedures. After adding the low-order polynomial terms, the boundary effect was reduced. The performance of the two functions was also compared. |
本系統中英文摘要資訊取自各篇刊載內容。