Simultaneous Inference for High-dimensional Linear Models
(2016)cite arxiv:1603.01295Comment: To appear in JASA -- T&M. First submission date: Oct, 2014.Аннотация
This paper proposes a bootstrap-assisted procedure to conduct simultaneous
inference for high dimensional sparse linear models based on the recent
de-sparsifying Lasso estimator (van de Geer et al. 2014). Our procedure allows
the dimension of the parameter vector of interest to be exponentially larger
than sample size, and it automatically accounts for the dependence within the
de-sparsifying Lasso estimator. Moreover, our simultaneous testing method can
be naturally coupled with the margin screening (Fan and Lv 2008) to enhance its
power in sparse testing with a reduced computational cost, or with the
step-down method (Romano and Wolf 2005) to provide a strong control for the
family-wise error rate. In theory, we prove that our simultaneous testing
procedure asymptotically achieves the pre-specified significance level, and
enjoys certain optimality in terms of its power even when the model errors are
non-Gaussian. Our general theory is also useful in studying the support
recovery problem. To broaden the applicability, we further extend our main
results to generalized linear models with convex loss functions. The
effectiveness of our methods is demonstrated via simulation studies.
Описание
Simultaneous Inference for High-dimensional Linear Models