Emmanuel Payebto Zoua:  Subsampling estimates of the Lasso distribution.

Adviser: Prof. Dr. Peter Bühlmann

September 2011

Abstract:

We investigate possibilities offered by subsampling to etimate the distribution of the Lasso estimator and construct confidence intervals/hypothesis tests. Despite being inferior to the bootstrap in terms of higher-order accuracy in situations where the later is consistent,subsampling offers the advantage to work under very weak assumptions.
Thus, building upon Knight and Fu (2000), we first study the asymptotics of the Lasso estimator in a low dimensional setting and prove that under an orthogonal design assumption, the finite sample component distributions converge to a limit in a mode allowing for consistency of subsampling confidence intervals. We give hints that this result holds in greater generality. In a high dimensional setting, we study the adaptive Lasso under assumption of partial orthogonality introduced by Huang, Ma and Zhang (2008) and use the partial oracle result in distribution to argue that subsampling should provide valid confidence intervals for nonzero parameters. Simulations studies confirm the validity of subsampling to construct confidence intervals, tests for null hypotheses and control the FWER through subsampled p-values in a low dimensional setting.
In the high dimensional setting, confidence intervals for nonzero coefficients are
slightly anticonservative and false positive rates are shown to be conservative.


Download pdf (968 KB)