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研究生:翁岳塘
研究生(外文):Yueh-Tang Weng
論文名稱:遞增式及遞減式局部多項式迴歸
論文名稱(外文):Incremental and Decremental Local Polynomial Regression
指導教授:黃文瀚黃文瀚引用關係陳律閎
指導教授(外文):Wen-Han HwangLu-Hung Chen
口試委員:江其衽
口試委員(外文):Ci-Ren Jiang
口試日期:2016-07-22
學位類別:碩士
校院名稱:國立中興大學
系所名稱:統計學研究所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2016
畢業學年度:104
語文別:英文
論文頁數:25
中文關鍵詞:局部多項式迴歸(LPR)遞增式計算大數據Woodbury matrix identity交叉驗證功能性主成份分析(FPCA)
外文關鍵詞:Local Polynomial Regression (Kernel Smoother)Incremental Comput- ing (Streaming)Big-DataWoodbury matrix identityCross-ValidationFunctional Principal Component Analysis (FPCA).
相關次數:
  • 被引用被引用:1
  • 點閱點閱:182
  • 評分評分:
  • 下載下載:30
  • 收藏至我的研究室書目清單書目收藏:2
局部多項式迴歸(LPR)是常用的無母數技巧,當物聯網(IoT)來臨時,遞增式計算將被受到關注,我們此篇論文提出的方法-遞增式局部多項式迴歸(ILPR),應用遞增式計算在局部多項式迴歸上,以及考慮數學中Woodbury matrix identity的概念並提出逼近遞增式局部多項式迴歸(AILPR)。在LPR中,選擇式當的代寬是必要的,在此利用交叉驗證(CV)達成目的,並利用類似ILPR的技巧及相同的逼近法,提出逼近K次交叉驗證(AKCV)。再者LPR已經被運用在新資料型態分析的過程,如:功能性主成份分析(FPCA),我們也應用留一驗證法(LooCV)在這領域,提出留一軌跡驗證法(LicoCV)和逼近留一軌跡驗證法(AlicoCV)。最後在模擬研究及資料分析上呈現上述提出方法的結果。

Local polynomial regression (LPR) is a common nonparametric technique. Incremental computing will be more concerned when the era of Internet of Things (IoT) comes. We not only apply incremental computing for LPR and name the process incremental LPR (ILPR), but also propose an approximated incremental LPR (AILPR). The main idea and mathematical skill on AILPR the approach are developed on the approximation in the special case of Woodbury matrix identity. Bandwidth selection is crucial in LPR. To avoid over_tting, one commonly considers a cross-validation (CV), we also develop an approximated K-fold CV (AKCV). Moreover, LPR is employed to perform some estimations in functional principal component analysis (FPCA) which is one of the most commonly employed approaches in functional/longitudinal data analysis. We extend leave-one-out CV (LooCV) for FPCA to conduct leave-i-curve-out CV (LicoCV) as well as an approximation version, approximated leave-i-curve-out CV (AlicoCV). The performance of our approaches, AILPR and AlicoCV are demonstrated with simulations and twenty traces of the handwriting data of "fda".

1. INTRODUCTION 1
2. METHODOLOGY 3
2.1. Framework for Local Polynomial Regression . . . . . . . . . . . . . . 3
2.2. Incremental Local Polynomial Regression . . . . . . . . . . . . . . . . 5
2.3. Approximated Incremental Local Polynomial Regression . . . . . . . 6
3. CROSS-VALIDATION 8
3.1. K-fold Cross-Validation for Local Polynomial Regression . . . . . . . 8
3.2. Approximated K-fold Cross-Validation for Local Polynomial Regression 9
3.3. Leave-one-out Cross-Validation for and
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