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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳宏 | |
| dc.contributor.author | Yen-Shiu Chin | en |
| dc.contributor.author | 金妍秀 | zh_TW |
| dc.date.accessioned | 2021-06-15T00:43:02Z | - |
| dc.date.available | 2008-09-02 | |
| dc.date.copyright | 2008-09-02 | |
| dc.date.issued | 2008 | |
| dc.date.submitted | 2008-08-29 | |
| dc.identifier.citation | References
[1] Bach, F. R. (2008). Consistency of the group Lasso and multiple kernel learning. Technical Report 00164735, HAL. [2] Bakin, S. (1999). Adaptive regression and model selection in data mining problem. PhD thesis, Australian National University, Australia. [3] David, H. A. and Nagaraja, H.N. (2003). Order Statistics, Third Edition. Wiley Interscience. [4] Durrett, R. (2005). Probability: Theory and Examples, Third Edition. Thomson. [5] H¨ardle, W. (1996). Search for significant variables in nonparametric additive regression.Biometrika 83, 541-549. [6] Hastie, T., Tibshirani, R. and Friedman, J. (2001). The Elements of Statistical Learning: Data Mining, Inference and Prediction, Springer Verlag. [7] Huang, H. H. (2007). Operating characteristics of Cp-LASSO on variable selection in linear regression with orthonormal regressors. Master Thesis, National Taiwan University, Taiwan. [8] Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995). Continuous Univariate Distributions, volume 2, Second Edition. Wiley. [9] Lancaster, H. O. (1969). The Chi-squared Distribution, First Edition. Wiley. [10] Mallows, C. L. (1973). Some comments on Cp. Technometrics, 15, 661-675. [11] Mallows, C. L. (1995). More comments on Cp. Technometrics, 37, 362-372. [12] Meier, L., van de Geer, S and B¨uhlmann, P. (2008). The group Lasso for logistic regression. J. R. Statist. Soc. B. 70, 53-71. [13] Royden, H. L. (1988). Real Analysis, Third Edition. Macmillan Publishing Company. [14] Stone, C. J. (1985). Additive regression and other nonparametric models. Ann. Statist., 13, 689-705. [15] Tibshirani, R. (1996). Regression shrinkage and selection via the Lasso. J. R. Statist. Soc. B, 58, 267-288. [16] Yuan, M. and Lin, Y. (2006). Model selection and estimation in regression with grouped variables. J. R. Statist. Soc. B. 68, 49-67. [17] Zhang P. (1992). On the distributional properties of model selection criteria. J. A. Statist. Asso.. 87, 732-737. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/42033 | - |
| dc.description.abstract | We consider the problem of selecting grouped variable in linear regression via the group Lasso and Mallows' Cp, especially when the columns in the full design matrix are orthogonal. We address two questions. Since Mallows' Cp is derived to be prediction optimal, how well the group Lasso coupled with Cp-criterion performs on selecting or dropping grouped variables? Since the group Lasso exploits additional group structure, will it perform better than Lasso on selecting the correct model? We propose that the behavior of the group Lasso coupled with Cp-criterion on selecting or dropping a grouped variable is like the detection of the grouped variable coming from χ2p or χ'2p. Moreover, we observe that the group Lasso coupled with Cp-criterion leads to a over-fitted regression model. The group structures do not always encourage us to select a better model when we compare that with Cp-Lasso. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T00:43:02Z (GMT). No. of bitstreams: 1 ntu-97-R94221041-1.pdf: 1868599 bytes, checksum: c344e108f0001bb0141c33a0151a74cd (MD5) Previous issue date: 2008 | en |
| dc.description.tableofcontents | Abstract v
1 Introduction 1 2 The group Lasso with Cp-criterion 3 3 Orthogonal design case 6 3.1 One-grouped variable 8 3.2 More on two-grouped variable 15 3.3 More on three-grouped variable 27 3.4 General case 36 4 Simulation studies 38 4.1 One-grouped variable 38 4.2 Two-grouped and three-grouped variable cases 39 5 Discussion 41 References 41 | |
| dc.language.iso | en | |
| dc.subject | Shrinkage | zh_TW |
| dc.subject | Group Lasso | zh_TW |
| dc.subject | Mallows' Cp | zh_TW |
| dc.subject | Group variable selection | zh_TW |
| dc.title | Variable Selection in Linear Regression with Group Structure via the Group Lasso and Mallows' Cp | zh_TW |
| dc.title | Variable Selection in Linear Regression with Group
Structure via the Group Lasso and Mallows' Cp | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 96-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳素雲,江金倉,張源俊 | |
| dc.subject.keyword | Group Lasso,Mallows' Cp,Group variable selection,Shrinkage, | zh_TW |
| dc.relation.page | 43 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2008-08-29 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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| ntu-97-1.pdf 未授權公開取用 | 1.82 MB | Adobe PDF |
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