政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/128560

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/128560

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Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/128560

Title:	兩種基於B-Spline迴歸模型之節點選取演算法比較 A comparative study of two knot selection algorithms for B-Spline regression
Authors:	王姿尹 Wang, Zih-Yin
Contributors:	黃子銘王姿尹 Wang, Zih-Yin
Keywords:	B-Spline迴歸模型節點選取 B-Spline tensor B-Spline regression model Knot selection B-Spline tensor
Date:	2019
Issue Date:	2020-02-05 17:07:25 (UTC+8)
Abstract:	本文聚焦於B-Spline迴歸模型之節點選取議題，分別以MSE(Mean Square Error)、MSE的變異數與節點估計時間為指標，比較兩種演算法估計效果、執行穩定度與執行效率之優劣。其一為Huang (2019)提出的演算法，它應用假設檢定由資料中尋找節點；其二參考Zhou and Shen (2001)的節點初始設定概念，並尋找節點最佳位置，同時，將兩種演算法推廣至雙變量可加性模型。依模擬結果可知，誤差大的單變量資料，以第一種演算法估計效果較佳且具高穩定度，但執行效率略慢；而誤差小的單變量資料，第二種演算法的估計效果有機會更佳，且兼具高穩定度與高執行效率。至於雙變量資料，若其中有較多反曲點，以第一種演算法估計效果較佳；反之，則適合以第二種演算法估計，然而，就執行效率而言，兩種演算法皆耗費多時。 This thesis focuses on the topic of knot selection for B-Spline regression model. Two algorithms, Algorithm 1 and Algorithm 2, are compared in terms of estimation accuracy, stability and computational cost. Algorithm 1 is based on the algorithm in Huang (2019), searching knots from data through statistical hypothesis. Algorithm 2 is based on the knot initialization in Zhou and Shen 2001). Furthermore, the two algorithms are extended to fit a bivariate additive model. According to the results of simulation studies, for univariate data with large errors, Algorithm 1 has better estimation accuracy, higher stability but is more computationally expensive; on the other hand, Algorithm 2 has better estimation accuracy, higher stability and is less computationally expensive when the errors become small. As for bivariate data, Algorithm 1 performs better than Algorithm 2 when the regression function has many reflection points. On the contrary, Algorithm 2 performs better when the regression function is smooth. However, this two algorithms are both time consuming.
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Description:	碩士國立政治大學統計學系 107354007
Source URI:	http://thesis.lib.nccu.edu.tw/record/#G0107354007
Data Type:	thesis
DOI:	10.6814/NCCU202000007
Appears in Collections:	[Department of Statistics] Theses

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