In this paper,we mainly study the feature screening and error variance estimation in ultrahigh-dimensional linear model with errors-in-variables(EV).Given that sure independence screening(SIS)method by marginal Pearso...In this paper,we mainly study the feature screening and error variance estimation in ultrahigh-dimensional linear model with errors-in-variables(EV).Given that sure independence screening(SIS)method by marginal Pearson’s correlation learning may omit some important observation variables due to measurement errors,a corrected SIS called EVSIS is proposed to rank the importance of features according to their corrected marginal correlation with the response variable.Also,a corrected error variance procedure is proposed to accurately estimate the error variance,which could greatly attenuate the influence of measurement errors and spurious correlations,simultaneously.Under some regularization conditions,the proposed EVSIS possesses sure screening property and consistency in ranking and the corrected error variance estimator is also proved to be asymptotically normal.The two methodologies are illustrated by some simulations and a real data example,which suggests that the proposed methods perform well.展开更多
基金supported partly by the National Natural Science Foundation of China(Grant No.11971324)supported by the State Key Program of National Natural Science Foundation of China(Grant No.12031016).
文摘In this paper,we mainly study the feature screening and error variance estimation in ultrahigh-dimensional linear model with errors-in-variables(EV).Given that sure independence screening(SIS)method by marginal Pearson’s correlation learning may omit some important observation variables due to measurement errors,a corrected SIS called EVSIS is proposed to rank the importance of features according to their corrected marginal correlation with the response variable.Also,a corrected error variance procedure is proposed to accurately estimate the error variance,which could greatly attenuate the influence of measurement errors and spurious correlations,simultaneously.Under some regularization conditions,the proposed EVSIS possesses sure screening property and consistency in ranking and the corrected error variance estimator is also proved to be asymptotically normal.The two methodologies are illustrated by some simulations and a real data example,which suggests that the proposed methods perform well.
