Before revision:  In the classic insertion-only model of data streams, Ben-Eliezer et. al. (PODS 2020, best paper award) show how to convert a non-robust algorithm into a robust one with a roughly 1/ overhead. This was subsequently improved to a 1/\sqrt{\varepsilon\mathcal{O}\left({\varepsilon^{4/p}}\cdot n^{1-2/p}}\right) \mathcal{O}\left({\varepsilon^{4/p}}\cdot n^{1-2/p}}\right)  the first optimal dependence on the approximation factor.
After revision:  In the classic insertion-only model of data streams, Ben-Eliezer et. al. (PODS 2020, best paper award) show how to convert a non-robust algorithm into a robust one with a roughly 1/ , then there exist space efficient algorithms with improved dependencies on the approximation parameter \varepsilon. In particular, for any real p > 2, we first obtain an algorithm for F_p moment estimation using\mathcal{O}\left({\varepsilon^{4/p}}\cdot n^{1-2/p}}\right) \mathcal{O}\left({\varepsilon^{4/p}}\cdot n^{1-2/p}}\right) the first optimal dependence on the approximation factor.