The desparsified lasso is a high-dimensional estimation method which provides uniformly valid inference. We extend this method to a time series setting under Near-Epoch Dependence (NED) assumptions allowing for non-Gaussian, serially correlated and heteroskedastic processes, where the number of regressors can possibly grow faster than the time dimension. We first derive an oracle inequality for the (regular) lasso, relaxing the commonly made exact sparsity assumption to a weaker alternative, which permits many small but non-zero parameters. The weak sparsity coupled with the NED assumption means this inequality can also be applied to the (inherently misspecified) nodewise regressions performed in the desparsified lasso. This allows us to establish the uniform asymptotic normality of the desparsified lasso under general conditions. Additionally, we show consistency of a long-run variance estimator, thus providing a complete set of tools for performing inference in high-dimensional linear time series models. Finally, we perform a simulation exercise to demonstrate the small sample properties of the desparsified lasso in common time series settings.

Some problems of epinephrine use in glaucoma are summarized, including side effects and increased responsiveness in POAG. -- DPE is a pro-drug that differs from epinephrine by the addition of two pivalyl side chains. This alteration provides a more lipophilic compound which penetrates the corneal barrier 17 times better. -- Fifteen POAG patients took part in a single-dose trial in order to determine the mydriatic and IOP-lowering effect of 0.2% DPE. DPE 0.2% is a potent mydriatic and lowers IOP approximately 10 times as efficiently as epinephrine. In view of the lower dose a reduction in systemic and ocular side effects may be expected.