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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 歐陽彥正(Yen-Jen Oyang) | - |
| dc.contributor.author | Rou-Jun Liu | en |
| dc.contributor.author | 劉柔均 | zh_TW |
| dc.date.accessioned | 2023-03-19T22:34:28Z | - |
| dc.date.copyright | 2022-09-06 | - |
| dc.date.issued | 2022 | - |
| dc.date.submitted | 2022-08-22 | - |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/84950 | - |
| dc.description.abstract | 核心密度估計方法(Kernel Density Estimation)是常見的無母數統計方法之一，相較於有母數統計，其不需要預先知道資料的分布假設，因此使用上具有較高的彈性。在核密度分析中，帶寬的選擇是影響結果的重要因素，因此如何挑選合適的帶寬成為重要的討論議題。 本研究改進 RVKDE 方法，使用最大概似估計法(Maximum Likelihood Estimation)來找出用來移動至經驗法則的最佳倍數，在多種人工合成資料集上實驗，將我們的方法與經驗法則、 Scott’s 法則、 Abramson提出的方法以及 ArcGIS 之方法進行比較，結果顯示雖然使用MLE 無法每一次都完全精準地找出真正的最優倍數，但距離正確的倍數亦不遠，且積分均方誤差(Mean Integrated Square Error)表現明顯優於其他常用的方法，估計結果的準確度大幅上升。 | zh_TW |
| dc.description.abstract | Kernel density estimation (KDE) is one of the most popular non-parametric methods to construct heatmap analysis. Due to the great influence on the result performance, the choice of bandwidth has become an important issue to discuss. This study improves Relaxed Variable Kernel Density Estimation (RVKDE) by implementing maximum likelihood estimation (MLE) to select the optimal multiple value of adjusted normal reference rule when shifting the median of bandwidth. We compare the performance of our method with the normal reference rule, Scott’s rule, the method proposed by Abramson, the method applied in ArcGIS, the original RVKDE method, and the improved ORAKDE method in 2-D and 3-D experiments. Although sometimes using MLE cannot precisely find out the exact optimal multiple number, it would not be far from the correct one and objectively provides an instructive suggestion of deciding the value. The measurement criteria Mean Integrated Square Error (MISE) of our method significantly outperforms than other methods, typically for the data whose patterns obviously differ from normal distribution. | en |
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U0001-2208202213401800.pdf: 1341817 bytes, checksum: c471567014e3bee8ecbbee217ebe3e2e (MD5) Previous issue date: 2022 | en |
| dc.description.tableofcontents | ABSTRACT ..................................................................... I 中文摘要 ..................................................................... II TABLE OF CONTENTS ........................................................... III LIST OF FIGURES .............................................................. V LIST OF TABLES ............................................................... VI CHAPTER 1 INTRODUCTION ....................................................... 1 1.1 Background ............................................................... 1 1.1.1 Density Estimation ..................................................... 1 1.1.2 Kernel Density Estimation .............................................. 2 1.2 Aim of The Study ......................................................... 4 1.3 Structure of the Thesis .................................................. 4 CHAPTER 2 LITERATURE REVIEW .................................................. 5 2.1 Kernel Function .......................................................... 5 2.2 Bandwidth Selection ...................................................... 6 2.2.1 Normal Reference Rule .................................................. 7 2.2.2 Scott’s Rule ........................................................... 8 2.2.3 Abramson ............................................................... 8 2.2.4 ArcGIS ................................................................. 9 2.2.5 RVKDE .................................................................. 10 2.2.6 ERAKDE ................................................................. 11 CHAPTER 3 METHOD ............................................................. 13 3.1 The Optimization Procedure ............................................... 13 3.2 Implementation Practices ................................................. 15 3.3 Performance Measurement .................................................. 16 CHAPTER 4 SIMULATION EXPERIMENTS ............................................. 17 4.1 Distributions of the 2-D datasets ........................................ 17 4.2 Distributions of the 3-D datasets ........................................ 20 4.3 Results .................................................................. 23 CHAPTER 5 DISCUSSION AND FUTURE WORK ......................................... 28 5.1 Discussion ............................................................... 28 5.2 Future Work .............................................................. 29 REFERENCE .................................................................... 30 APPENDIXⅠ .................................................................... 34 APPENDIXⅡ .................................................................... 36 | - |
| dc.language.iso | en | - |
| dc.subject | 核密度估計 | zh_TW |
| dc.subject | 帶寬選擇 | zh_TW |
| dc.subject | 最大概似估計法 | zh_TW |
| dc.subject | Kernel Density Estimation | en |
| dc.subject | Maximum Likelihood Estimation | en |
| dc.subject | Bandwidth Selection | en |
| dc.title | 針對變量核心密度估計之帶寬設定進行最佳化之研究 | zh_TW |
| dc.title | A Study on Optimal Bandwidth Settings for Adaptive Kernel Density Estimation | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 110-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 蔡政安(Chen-An Tsai catsai@ntu.edu.tw) | - |
| dc.subject.keyword | 核密度估計,帶寬選擇,最大概似估計法, | zh_TW |
| dc.subject.keyword | Kernel Density Estimation,Bandwidth Selection,Maximum Likelihood Estimation, | en |
| dc.relation.page | 37 | - |
| dc.identifier.doi | 10.6342/NTU202202644 | - |
| dc.rights.note | 同意授權(限校園內公開) | - |
| dc.date.accepted | 2022-08-23 | - |
| dc.contributor.author-college | 共同教育中心 | zh_TW |
| dc.contributor.author-dept | 統計碩士學位學程 | zh_TW |
| dc.date.embargo-lift | 2022-09-06 | - |
| 顯示於系所單位： | 統計碩士學位學程 | |
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