We consider the problem of robustly testing the norm of a high-dimensional sparse signal vector under two different observation models. In the first model, we are given $n$ i.i.d.

We consider the problem of robustly testing the norm of a high-dimensional sparse signal vector under two different observation models. In the first model, we are given n i.i.d. We show that any algorithm for this task requires n \Omega\left(s\log\frac{ed}{s}\right) samples, which is tight up to logarithmic factors. We also extend our results to other common notions of sparsity, namely, \ \theta\ _q\le s for any 0 q 2 . In the second observation model that we consider, the data is generated according to a sparse linear regression model, where the covariates are i.i.d.