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| 研究生： |
王逸閎 WANG, YI-HONG |
|---|---|
| 論文名稱： |
高維度邏輯回歸的模型選擇與參數估計 Model Selection in High-Dimensional Logistic Regression and Parameter Estimation |
| 指導教授： |
銀慶剛
Ing, Ching-Kang |
| 口試委員: |
俞淑惠
Yu, Shu-Hui 冼芻蕘 Sin, Chor-Yiu 黃學涵 Huang, Hsueh-Han |
| 學位類別： |
碩士 Master |
| 系所名稱： |
理學院 - 統計學研究所 Institute of Statistics |
| 論文出版年： | 2024 |
| 畢業學年度： | 112 |
| 語文別： | 英文 |
| 論文頁數： | 34 |
| 中文關鍵詞： | 高維度低樣本的邏輯迴歸 、加權正交貪婪算法 、高維信息準則 、模型選擇 |
| 外文關鍵詞： | High dimension low sample size logistic regression, Weighted orthogonal greedy algorithm, High-dimensional informational criterion, Model selection |
| 相關次數： | 點閱：48 下載：0 |
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高維低樣本量數據中的模型選擇在過去幾十年中對許多統計方法提出了巨大挑戰。為了處理這些數據，我們開發了受Ing和Lai (2011) 提出的三階段模型選擇啟發的模型選擇程序。在Ing和Lai (2011) 中，他們使用正交貪婪算法 (OGA) 來選擇線性模型中的變數，並結合高維信息準則 (HDIC) 和修剪來去除冗餘變數。對於這篇文章中的三階段方法，OGA + HDIC + 修剪，我們關注的是第一階段中選擇變數的功能。我們通過在平方誤差和中添加權重來調整正交貪婪算法 (OGA)，使其適應非線性邏輯模型。此外，我們還提出了負對數概似函數作為新函數。在選擇變數後，我們使用HDIC和修剪來去除冗餘變數。模擬和真實數據分析的結果表明，我們的方法具有實用性和有效性。
Model selection in high-dimension low-sample-size data has posed great challenges to many statistical methods over the past decades. To handle these data, we developed our model selection procedure inspired by the three-stage model selection proposed by Ing and Lai (2011). In Ing and Lai (2011), they make use of the orthogonal greedy algorithm (OGA) to select variables in a linear model and combine it with high-dimensional information criteria (HDIC) and trim to remove redundant variables. For the three-stage method, OGA + HDIC + trim, in this article, we focus on the function in the first stage to select variables. We adjusted the orthogonal greedy algorithm (OGA) by adding weights in the sum of squared errors to make it adapt to a nonlinear logistic model. Moreover, we also propose negative log likelihood as a new function. After selecting variables, we use HDIC and trim to remove redundant variables. The results of simulations and real data analysis show that our method demonstrates usefulness and practicality.
1. Imori,S., Ing,C.-K. (2023), Prediction and variable selection in high-dimensional misspecified regression models under variable shift,Working paper.
2. Lin, C.-T., Ing,C.-K. and Dai, C.-S. (2023), High-dimensional model selection via Chebyshev’s Greedy Algorithm,Working paper.
3. Ing,C.-K. and Lai,T.-L.(2011), A stepwise regression method and consistent model selection for high-dimensional sparse linear model,Statistica Sinica, 21, 1473-1513.
4. Czepiel, S.A. (2002), Maximum Likelihood Estimation of Logistic Regression Models: Theory and Implementation. https://czep.net/stat/mlelr.pdf
5. Dobson, A.J., Barnet,A.G.(1990), Estimation,An Introduction to Generalized Linear Models, Chapman and Hall, 65-76