The focus of modern biomedical studies has gradually shifted to explanation
and estimation of joint effects of high dimensional predictors on disease
risks. Quantifying uncertainty in these estimates may provide valuable insight
into prevention strategies or treatment decisions for both patients and
physicians. High dimensional inference, including confidence intervals and
hypothesis testing, has sparked much interest. While much work has been done in
the linear regression setting, there is lack of literature on inference for
high dimensional generalized linear models. We propose a novel and
computationally feasible method, which accommodates a variety of outcome types,
including normal, binomial, and Poisson data. We use a "splitting and
smoothing" approach, which splits samples into two parts, performs variable
selection using one part and conducts partial regression with the other part.
Averaging the estimates over multiple random splits, we obtain the smoothed
estimates, which are numerically stable. We show that the estimates are
consistent, asymptotically normal, and construct confidence intervals with
proper coverage probabilities for all predictors. We examine the finite sample
performance of our method by comparing it with the existing methods and
applying it to analyze a lung cancer cohort study