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研究生:黃學涵
研究生(外文):Hsueh-Han Huang
論文名稱:高維度時間序列並帶有測量誤差模型之模型選擇
論文名稱(外文):Model Selection for High-Dimensional Time Series Models with Measurement Errors
指導教授:銀慶剛銀慶剛引用關係
口試委員:俞淑惠黃信誠徐南蓉鄭又仁
口試日期:2017-06-09
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:應用數學科學研究所
學門:數學及統計學門
學類:其他數學及統計學類
論文種類:學術論文
論文出版年:2017
畢業學年度:105
語文別:英文
論文頁數:30
中文關鍵詞:高維度測量誤差正交化貪婪演算法稀疏性時間序列
外文關鍵詞:High-dimensionalmeasurement errorOGAsparsitytime series
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We use a fast stepwise regression method, called orthogonal greedy algorithm (OGA) to select variables for high-dimensional time series model with measurement errors. Under a weak sparsity condition, we derive a convergence rate of OGA, which is expressed in terms of the number of iterations, the sample size and the order of the moment imposed on the error process. Under a strong sparsity condition, we develop a consistent model selection procedure using OGA and a high-dimensional information criterion.
中文摘要………………………………………………………………………… i
英文摘要…………………………………………………………………………. ii
1.Introduction………………………………………………………………….. 1
2.OGA and Noiseless OGA……………………………………………….. 3
3.Uniform Convergence Rate of Empirical Prediction Error……………………... 4
4.Sure Screening Property and Model Selection Consistency…………………….. 9
5.Simulation Studies……………………………………………….. 16
參考文獻…………………………………………………………………….…… 23
附錄………………………………………………………………………..………. .24
Abhirup Datta and Hui Zou. (2016). CoCoLasso for High-dimensional Error-in-variables Regression. https://arxiv.org/abs/1510.07123.

Alexandre Belloni, Mathieu Rosenbaum and Alexandre B.Tsybakov.(2014). An {l1; l2; linfinite}-Regularization Approach to High-Dimensional Errors-in-variables Models. https://arxiv.org/abs/1412.7216.

Alexandre Belloni, Mathieu Rosenbaum and Alexandre B.Tsybakov. (2016). Linear and Conic Programming Estimators in High-Dimensional Errors-in variables Models. https://arxiv.org/abs/1408.0241.

Ching-Kang Ing and Tze Leung Lai (2011). A stepwise regression method and consistent model selection for high-dimensional sparse linear models. Statist.Sinica,1473-1513.

Ching-Kang Ing and Kunling Huang (2016). Model Selection for High-Dimensional Multivariate Time Dependent Models (Unpublished master''s thesis). National Taiwan University, Taipei City.

C.Z.Wei. (1987). Adaptive prediction by least squares predictors in stochastic regression models with applications to time series. Ann.Statist.15(4):1667-1682.

David F.Findley and Ching-Zong Wei.(1993).Moment bounds for deriving time series CLTs and model selection procedures. Statist.Sinica,453-480.

Po-Ling Loh and Martin J. Wainwright.(2012).High-dimensional regression with noisy and missing data:Provable guarantees with nonconvexity. Ann.Statist.40(3):1637-1664.

Temlyakov,V.N .(2000).Weak greedy algorithms. Adv.Comput.Math.12,213-227.
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