We propose a new method, semi-penalized inference with
direct false discovery rate control (SPIDR), for
variable selection and confidence interval construction
in high-dimensional linear regression. SPIDR first uses
a semi-penalized approach to constructing estimators of
the regression coefficients. We show that the SPIDR
estimator is ideal in the sense that it equals an ideal
least squares estimator with high probability under a
sparsity and other suitable conditions. Consequently,
the SPIDR estimator is asymptotically normal.
Based on this distributional result, SPIDR determines
the selection rule by directly controlling false discovery
rate. This provides an explicit assessment of the
selection error. This also naturally leads to confidence
intervals for the selected coefficients with a proper
confidence statement. We conduct simulation studies to
evaluate its finite sample performance and demonstrate
its application on a breast cancer gene expression data
set. Our simulation studies and data example suggest
that SPIDR is a useful method for high-dimensional
statistical inference in practice.