this is for holding javascript data
Vadim Kosoy edited The_following_theorem_is_the__.tex
about 8 years ago
Commit id: 03bfca25e88d0952a03ab38d14a64a9e52daf69c
deletions | additions
diff --git a/The_following_theorem_is_the__.tex b/The_following_theorem_is_the__.tex
index 59d43e2..a603c2b 100644
--- a/The_following_theorem_is_the__.tex
+++ b/The_following_theorem_is_the__.tex
...
\begin{theorem}
\label{thm:ort}
Fix
$\Gamma$ $\Gamma=(\Gamma_{\mathfrak{R}}$, $\Gamma_{\mathfrak{A}})$ a pair of growth spaces of rank 2 and $\mathcal{E}$ an error space of rank 2. Assume there is $\zeta \in \mathcal{E}$ s.t. $\log \max(-\log \zeta, 1) \in
\Gamma_2$\footnote{If \Gamma_{\mathfrak{A}})$\footnote{If $\log(k+1), \log(j+1) \in
\Gamma_2$ \Gamma_{\mathfrak{A}})$ then this condition holds for any $\mathcal{E}$ since we can take $\zeta = 2^{-h}$ for $h$ polynomial.}. Consider $(\mu,f)$ a distributional estimation problem and $P$ an $\mathcal{E}(\Gamma)$-optimal predictor for $(\mu,f)$. Then, $P$ is also an $\mathcal{E}^{\frac{1}{2}\sharp}(\Gamma)$-optimal predictor for $(\mu,f)$.
\end{theorem}