Empirical Approximation of $L_p$ Norms

Feng Dai, Egor Kosov, Noel Murasko

We study empirical $L_p$ moments of a random vector $\ddot{I}†$ based on its i.i.d.\ copies $\ddot{I}{†}^1,\dots ,\ddot{I}{†}^m$, that is, $\frac{1}{m}{\sum }_{j=1}^m|⟨\ddot{I}{†}^j,y⟩{|}^p$. O…