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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/82023完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 丘政民(Jeng-Min Chiou) | |
| dc.contributor.author | Che-Wei Hsu | en |
| dc.contributor.author | 許哲維 | zh_TW |
| dc.date.accessioned | 2022-11-25T05:34:16Z | - |
| dc.date.available | 2026-07-30 | |
| dc.date.copyright | 2021-08-20 | |
| dc.date.issued | 2021 | |
| dc.date.submitted | 2021-08-03 | |
| dc.identifier.citation | Chen, C. W. S., Chan, J. S. K., Gerlach, R., and Hsieh, W. Y. L. A comparison of estimators for regression models with change points. Statistics and Computing 21, 3 (2011), 395-414. Das, R., Banerjee, M., Nan, B., and Zheng, H. Y. Fast estimation of regression parameters in a broken-stick model for longitudinal data. Journal of the American Statistical Association 111, 515 (2016), 1132-1143. Delicado, P. Dimensionality reduction when data are density functions. Computational Statistics Data Analysis 55, 1 (2011), 401-420. Kneip, A., and Utikal, K. J. Inference for density families using functional principal component analysis. Journal of the American Statistical Association 96, 454 (2001), 519-542. Lerman, P. M. Fitting segmented regression models by grid search. Journal of the Royal Statistical Society. Series C (Applied Statistics) 29, 1 (1980), 77-84. Loane, M., Morris, J. K., Addor, M.-C., Arriola, L., Budd, J., Doray, B., Garne, E., Gatt, M., Haeusler, M., and Khoshnood, B. Twenty-year trends in the prevalence of down syndrome and other trisomies in europe: impact of maternal age and prenatal screening. European Journal of Human Genetics 21, 1 (2013), 27-33. Mazuy, M., Barbieri, M., Breton, D., and d'Albis, H. Recent demographic developments in France: a decline in fertility, an increase in mortality. Population 71, 3 (2016), 395-453. Petersen, A., and Muller, H.-G. Functional data analysis for density functions by transformation to a Hilbert space. The Annals of Statistics 44, 1 (2016). Petersen, A., and M uller, H.-G. Frechet regression for random objects with Euclidean predictors. The Annals of Statistics 47, 2 (2019), 691-719. Tishler, A., and Zang, I. A new maximum-likelihood algorithm for piecewise regression. Journal of the American Statistical Association 76, 376 (1981), 980-987. Wang, J.-L., Chiou, J.-M., and Muller, H.-G. Functional data analysis. Annual Review of Statistics and Its Application 3, 1 (2016), 257-295. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/82023 | - |
| dc.description.abstract | 分段線性模型是專門用來刻劃當應變數隨著解釋變數在變動時遇到明顯轉折的現象。在論文中，我們提出了一個當應變數為機率密度函數的分段線性迴歸模型，這個模型的目標在於找出當應變數為機率密度函數時迴歸直線上的斷點，以及提供當機率密度函數隨著解釋變數變動時的線性視覺化圖形。我們透過對於機率密度函數的函數主成分分析，以及對於每個斷點做平滑化的技巧，去進行迴歸係數的估計，最後利用牛頓法將迴歸係數以及斷點的位置估計出來。此外，在論文中，我們將對於此模型在估計斷點的準確度，以及預測上的表現，利用不同的估計方法去做比較。最後，我們將所提出的分段線性模型應用在真實世界的資料當中。 | zh_TW |
| dc.description.provenance | Made available in DSpace on 2022-11-25T05:34:16Z (GMT). No. of bitstreams: 1 U0001-2907202114180700.pdf: 3099375 bytes, checksum: a73ff7af242c67bbad7628f7ea60e585 (MD5) Previous issue date: 2021 | en |
| dc.description.tableofcontents | 1 Introduction 1 2 Methodology 5 2.1 Preliminaries 5 2.2 The piecewise density regression model 6 3 Estimation 10 3.1 Functional principal component analysis for density responses 10 3.2 Estimation of the model components 11 4 Simulation 13 4.1 Simulation settings 13 4.2 Simulation results 15 4.3 Sensitive analysis on selecting $\gamma_n$ 18 5 Data application 21 5.1 Density estimation 21 5.2 Data application results 22 6 Conclusion 24 Reference 25 | |
| dc.language.iso | en | |
| dc.subject | 迴歸分析 | zh_TW |
| dc.subject | 分段線性模型 | zh_TW |
| dc.subject | 機率密度函數 | zh_TW |
| dc.subject | Piecewise linear model | en |
| dc.subject | Density | en |
| dc.subject | Regression analysis | en |
| dc.title | 對於機率密度函數之分段線性模型 | zh_TW |
| dc.title | A Piecewise Linear Model for Density Functions | en |
| dc.date.schoolyear | 109-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 江金倉(Hsin-Tsai Liu),李彥寰(Chih-Yang Tseng),蔡碧紋 | |
| dc.subject.keyword | 分段線性模型,機率密度函數,迴歸分析, | zh_TW |
| dc.subject.keyword | Piecewise linear model,Density,Regression analysis, | en |
| dc.relation.page | 26 | |
| dc.identifier.doi | 10.6342/NTU202101894 | |
| dc.rights.note | 同意授權(限校園內公開) | |
| dc.date.accepted | 2021-08-04 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 應用數學科學研究所 | zh_TW |
| dc.date.embargo-lift | 2026-07-30 | - |
| 顯示於系所單位： | 應用數學科學研究所 | |
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|---|---|---|---|
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