diff --git a/semester4/ps/ps-rb/main.pdf b/semester4/ps/ps-rb/main.pdf index 531bdc3..35abd01 100644 Binary files a/semester4/ps/ps-rb/main.pdf and b/semester4/ps/ps-rb/main.pdf differ diff --git a/semester4/ps/ps-rb/parts/06_stats.tex b/semester4/ps/ps-rb/parts/06_stats.tex index 4499f2b..24aa4c7 100644 --- a/semester4/ps/ps-rb/parts/06_stats.tex +++ b/semester4/ps/ps-rb/parts/06_stats.tex @@ -9,3 +9,17 @@ $$ T_l = t_l\Bigl( X_1,\ldots,X_n \Bigr) $$ \smalltext{$t_l$ heisst Schätzfunktion, eine Auswertung $T_l(\omega)$ heisst Schätzwert} + +\definition \textbf{Erwartungstreu} +$$ + T \text{ Erwartungstreu } \iffdef \forall \vartheta \in \Theta:\quad \E_\vartheta\bigl[ T \bigr] = \vartheta +$$ + +\definition \textbf{Bias} $\quad\E_\vartheta[T] - \vartheta$ + +\definition \textbf{MSE} $\quad\text{MSE}_\vartheta[T] = \E_\vartheta\bigl[ (T-\vartheta)^2 \bigr]$ + +% def Schätzerfolgen / konsistent + +% bmk 7.7: zerlegung MSE +