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Consistency of $ell_{1}$ penalized high-dimensional regressions
发布时间:2017-12-27     点击次数:
报告题目: Consistency of $ell_{1}$ penalized high-dimensional regressions
报 告 人: 谢芳 博士( 澳门大学 )
报告时间: 2018年01月03日 10:30--11:30
报告地点: 理学院东北楼四楼报告厅(404)
报告摘要:

This talk concerns consistency of the estimators of $ell_{1}$ penalized high-dimensional regressions including linear regressions and generalized linear regressions. For linear regressions, we consider the linear models with weakly dependent errors, such as $alpha$-mixing, $rho$-mixing error sequences. We prove that the estimators obtained by lasso and square-root lasso are consistent even in the non-Gaussian error case. For generalized linear regressions, we propose a new penalized method to solve sparse Poisson regression problems. It can be viewed as penalized weighted score function method, which possesses a tuning-free feature. We show that under mild conditions, our estimator is $ell_{1}$ consistent and the tuning parameter can be pre-specified, which enjoys the same good property as the square-root lasso.

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