Empirical Approximation of $L_p$ Norms

Feng Dai, Egor Kosov, Noel Murasko

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