Asymptotic properties of bridge estimators in sparse high-dimensional regression models

Details Asymptotic properties of bridge estimators in sparse high-dimensional regression models Asymptotic properties of bridge estimators in sparse high-dimensional regression models

2008-04-04

arxiv.org/abs/0804.0693v1

Annals of Statistics 2008, Vol. 36, No. 2, 587-613

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/009053607000000875 the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053607000000875

We study the asymptotic properties of bridge estimators in sparse, high-dimensional, linear regression models when the number of covariates may increase to infinity with the sample size. We are particularly interested in the use of bridge estimators to distinguish between covariates whose coefficients are zero and covariates whose coefficients are nonzero. We show that under appropriate conditions, bridge estimators correctly select covariates with nonzero coefficients with probability converging to one and that the estimators of nonzero coefficients have the same asymptotic distribution that they would have if the zero coefficients were known in advance. Thus, bridge estimators have an oracle property in the sense of Fan and Li [J. Amer. Statist. Assoc. 96 (2001) 1348--1360] and Fan and Peng [Ann. Statist. 32 (2004) 928--961]. In general, the oracle property holds only if the number of covariates is smaller than the sample size. However, under a partial orthogonality condition in which the covariates of the zero coefficients are uncorrelated or weakly correlated with the covariates of nonzero coefficients, we show that marginal bridge estimators can correctly distinguish between covariates with nonzero and zero coefficients with probability converging to one even when the number of covariates is greater than the sample size.

Affiliated with

Also associated with

No associations

Rating

Asymptotic properties of bridge estimators in sparse high-dimensional regression models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Asymptotic properties of bridge estimators in sparse high-dimensional regression models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Asymptotic properties of bridge estimators in sparse high-dimensional regression models will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-190770