Oracle inequalities for weighted group lasso in high-dimensional misspecified Cox models
Abstract We study the nonasymptotic properties of a general norm penalized estimator, which include Lasso, weighted Lasso, and group Lasso as special cases, for sparse high-dimensional misspecified Cox models with time-dependent covariates. Under suitable conditions on the true regression coefficien...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-11-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-020-02517-3 |
| _version_ | 1828932867224240128 |
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| author | Yijun Xiao Ting Yan Huiming Zhang Yuanyuan Zhang |
| author_facet | Yijun Xiao Ting Yan Huiming Zhang Yuanyuan Zhang |
| author_sort | Yijun Xiao |
| collection | DOAJ |
| description | Abstract We study the nonasymptotic properties of a general norm penalized estimator, which include Lasso, weighted Lasso, and group Lasso as special cases, for sparse high-dimensional misspecified Cox models with time-dependent covariates. Under suitable conditions on the true regression coefficients and random covariates, we provide oracle inequalities for prediction and estimation error based on the group sparsity of the true coefficient vector. The nonasymptotic oracle inequalities show that the penalized estimator has good sparse approximation of the true model and enables to select a few meaningful structure variables among the set of features. |
| first_indexed | 2024-12-14T01:08:13Z |
| format | Article |
| id | doaj.art-761310f14adc404ca1be1c1c8c92263c |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-14T01:08:13Z |
| publishDate | 2020-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-761310f14adc404ca1be1c1c8c92263c2022-12-21T23:22:53ZengSpringerOpenJournal of Inequalities and Applications1029-242X2020-11-012020113310.1186/s13660-020-02517-3Oracle inequalities for weighted group lasso in high-dimensional misspecified Cox modelsYijun Xiao0Ting Yan1Huiming Zhang2Yuanyuan Zhang3School of Mathematical Sciences and Center for Statistical Science, Peking UniversityDepartment of Statistics, Central China Normal UniversityDepartment of Mathematics, Faculty of Science and Technology, University of MacauCenter for Statistical Science, Tsinghua UniversityAbstract We study the nonasymptotic properties of a general norm penalized estimator, which include Lasso, weighted Lasso, and group Lasso as special cases, for sparse high-dimensional misspecified Cox models with time-dependent covariates. Under suitable conditions on the true regression coefficients and random covariates, we provide oracle inequalities for prediction and estimation error based on the group sparsity of the true coefficient vector. The nonasymptotic oracle inequalities show that the penalized estimator has good sparse approximation of the true model and enables to select a few meaningful structure variables among the set of features.https://doi.org/10.1186/s13660-020-02517-3Proportional hazard modelPartial likelihoodTime-dependent dataWeighted group LassoOracle inequalitiesSuprema of empirical processes |
| spellingShingle | Yijun Xiao Ting Yan Huiming Zhang Yuanyuan Zhang Oracle inequalities for weighted group lasso in high-dimensional misspecified Cox models Journal of Inequalities and Applications Proportional hazard model Partial likelihood Time-dependent data Weighted group Lasso Oracle inequalities Suprema of empirical processes |
| title | Oracle inequalities for weighted group lasso in high-dimensional misspecified Cox models |
| title_full | Oracle inequalities for weighted group lasso in high-dimensional misspecified Cox models |
| title_fullStr | Oracle inequalities for weighted group lasso in high-dimensional misspecified Cox models |
| title_full_unstemmed | Oracle inequalities for weighted group lasso in high-dimensional misspecified Cox models |
| title_short | Oracle inequalities for weighted group lasso in high-dimensional misspecified Cox models |
| title_sort | oracle inequalities for weighted group lasso in high dimensional misspecified cox models |
| topic | Proportional hazard model Partial likelihood Time-dependent data Weighted group Lasso Oracle inequalities Suprema of empirical processes |
| url | https://doi.org/10.1186/s13660-020-02517-3 |
| work_keys_str_mv | AT yijunxiao oracleinequalitiesforweightedgrouplassoinhighdimensionalmisspecifiedcoxmodels AT tingyan oracleinequalitiesforweightedgrouplassoinhighdimensionalmisspecifiedcoxmodels AT huimingzhang oracleinequalitiesforweightedgrouplassoinhighdimensionalmisspecifiedcoxmodels AT yuanyuanzhang oracleinequalitiesforweightedgrouplassoinhighdimensionalmisspecifiedcoxmodels |