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| 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: | [統計學系] 學位論文
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