  This paper proposes a decorrelation-based approach to test hypotheses and
construct confidence intervals for the low dimensional component of high
dimensional proportional hazards models. Motivated by the geometric projection
principle, we propose new decorrelated score, Wald and partial likelihood ratio
statistics. Without assuming model selection consistency, we prove the
asymptotic normality of these test statistics, establish their semiparametric
optimality. We also develop new procedures for constructing pointwise
confidence intervals for the baseline hazard function and baseline survival
function. Thorough numerical results are provided to back up our theory.
