Title: On Estimation of $L_{r}$-Norms in Gaussian White Noise Models,
Abstract: We provide a complete picture of asymptotically minimax estimation of
$L_r$-norms (for any $r\ge 1$) of the mean in Gaussian white noise model over
Nikolskii-Besov spaces. In this regard, we complement the work of Lepski,
Nemirovski and Spokoiny (1999), who considered the cases of $r=1$ (with
poly-logarithmic gap between upper and lower bounds) and $r$ even (with
asymptotically sharp upper and lower bounds) over Hölder spaces. We
additionally consider the case of asymptotically adaptive minimax estimation
and demonstrate a difference between even and non-even $r$ in terms of an
investigator's ability to produce asymptotically adaptive minimax estimators
without paying a penalty.