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| Title: | LASSO迴歸在B-spline基底組成之危險函數上的應用
Application of LASSO regression in estimating B-Spline-Based hazard functions |
| Authors: | 林子元
Lin, Zi-Yuan |
| Contributors: | 黃子銘
Huang, Tzee-Ming
林子元
Lin, Zi-Yuan |
| Keywords: | 比例危險模型
B樣條
Group lasso
拔靴法
Proportional hazards model
B-splines
Group lasso
Bootstrap |
| Date: | 2017 |
| Issue Date: | 2017-04-05 15:35:28 (UTC+8) |
| Abstract: | 一項關於比例危險模型的重要假設為對數危險函數與共變量之間的關係是線性的，本文探討當此假設不成立時，使用B樣條基底函數來近似共變量的非線性函數是可行的。在估計上，本文應用了group lasso方法。在適當的懲罰係數之下，對於不具解釋力的共變量而言，此方法可使對應至該共變量的一組基底係數同時估為零，以避免模型難以解讀的狀況。此外，本文嘗試為所提模型發展假設檢定。考慮的檢定量除了一般的Wald檢定量、概似比檢定量與分數檢定量之外，尚包括了因應懲罰項而作校正的檢定量與基於拔靴法的檢定量。本文採用模擬的方法比較各檢定量的優劣。
A strong assumption in the Cox proportional hazards model requires linearity of the covariates on the log hazard function. However, this assumption may be violated in practice. Alternatively, it is feasible to model the nonlinear effect via a combination of B-spline basis functions. In estimating the basis coefficients, the group lasso is applied. By so doing, a group of coefficients can be set zero simultaneously if the corresponding covariate is not predictive. Lastly, I develop hypothesis testing regarding this model. In addition to the ordinary Wald statistic, likelihood ratio statistic, and score statistic, two other types of testing statistic are considered: one adjust for penalty function and the other one based on bootstrap samples. Simulation studies are carried out to evaluate the performance of the proposed statistics. |
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| Description: | 碩士
國立政治大學
統計學系
103354014 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G1033540143 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
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