= Mean-estimation minimax lower bound for continuous densities
{title2=$R_n^*\geq1/(1152n)$}
For estimating the <expected value> over all continuous <probability density functions> on $[0,1]$, compare $f=1$ and $g_n(u)=1+(u-1/2)/\sqrt n$. Their means differ by $1/(12\sqrt n)$, and $\chi^2(P_{g_n}\Vert P_f)=1/(12n)$. The <chi-squared divergence of product measures> bounds joint <total variation distance> by $1/2$. The <metric squared-loss two-point bound> then gives the displayed uniform <minimax risk> lower bound.
Back to article page
