Bump macros to 92f54bf and use prederrf for prediction errors

_subfiles/_def-prediction-error.qmd

@@ -6,7 +6,7 @@ the observed [outcome](#def-outcome) $\Outvar$ of a [new observation](#def-new-o
 not the [conditional mean](#def-cond-expectation-function) of that outcome.
 The **prediction error** of $\predfn$ is the prediction minus that outcome:
 
-$$\esterr{\predfnf{\Predvar}}{\Outvar} \eqdef \predfnf{\Predvar} - \Outvar$$
+$$\prederrf{\predfn} \eqdef \predfnf{\Predvar} - \Outvar$$
 
 :::
 
@@ -17,7 +17,7 @@ $$\esterr{\predfnf{\Predvar}}{\Outvar} \eqdef \predfnf{\Predvar} - \Outvar$$
 
 In @exr-best-predictor,
 consider the constant [prediction](#def-prediction) $\predfn_1\paren{\Predvar} = 3$.
-Its [prediction error](#def-prediction-error) is $\esterr{\predfn_1\paren{\Predvar}}{\Outvar} = 3 - \Outvar$.
+Its [prediction error](#def-prediction-error) is $\prederrf{\predfn_1} = 3 - \Outvar$.
 This is $3$ when $\Outvar = 0$.
 It is $-3$ when $\Outvar = 6$.
 

_subfiles/_def-squared-error-risk.qmd

@@ -5,7 +5,7 @@ The **squared-error risk** of a prediction function $\predfnf{\Predvar}$,
 also called its **expected prediction error** [@hastie2009elements, p. 18],
 is the expected square of its [prediction error](#def-prediction-error):
 
-$$\popriskf{\predfn} \eqdef \E{\sqf{\esterr{\predfnf{\Predvar}}{\Outvar}}}$$
+$$\popriskf{\predfn} \eqdef \E{\sqf{\prederrf{\predfn}}}$$
 
 It is the [risk](#def-risk) under [squared error loss](#def-squared-error-loss).
 

_subfiles/_lem-cross-term-zero.qmd

@@ -4,7 +4,7 @@
 Let $\truemeanf{\Predvar} \eqdef \E{\Outvar \mid \Predvar}$ be the [conditional expectation function](#def-cond-expectation-function) of $\Outvar$ given $\Predvar$.
 For any [prediction function](#def-prediction) $\predfnf{\Predvar}$ with $\E{\predfnf{\Predvar}^2} < \infty$:
 
-$$\E{\esterr{\truemeanf{\Predvar}}{\Outvar} \cd \paren{\predfnf{\Predvar} - \truemeanf{\Predvar}}} = 0$$
+$$\E{\prederrf{\truemean} \cd \paren{\predfnf{\Predvar} - \truemeanf{\Predvar}}} = 0$$
 
 :::
 
@@ -15,11 +15,11 @@ by @thm-cond-pull-out it factors out of the [conditional expectation](#def-cond-
 
 $$
 \ba
-\E{\esterr{\truemeanf{\Predvar}}{\Outvar}\paren{\predfnf{\Predvar} - \truemeanf{\Predvar}} \mid \Predvar}
-&= \paren{\predfnf{\Predvar} - \truemeanf{\Predvar}} \cd \E{\esterr{\truemeanf{\Predvar}}{\Outvar} \mid \Predvar}
+\E{\prederrf{\truemean}\paren{\predfnf{\Predvar} - \truemeanf{\Predvar}} \mid \Predvar}
+&= \paren{\predfnf{\Predvar} - \truemeanf{\Predvar}} \cd \E{\prederrf{\truemean} \mid \Predvar}
 && \text{(a function of } \Predvar \text{ factors out)} \\
 &= \paren{\predfnf{\Predvar} - \truemeanf{\Predvar}} \cd \E{\truemeanf{\Predvar} - \Outvar \mid \Predvar}
-&& \text{(definition of } \esterr{\truemeanf{\Predvar}}{\Outvar} \text{)} \\
+&& \text{(definition of } \prederrf{\truemean} \text{)} \\
 &= \paren{\predfnf{\Predvar} - \truemeanf{\Predvar}} \cd \paren{\E{\truemeanf{\Predvar} \mid \Predvar} - \E{\Outvar \mid \Predvar}}
 && \text{(linearity of conditional expectation)} \\
 &= \paren{\predfnf{\Predvar} - \truemeanf{\Predvar}} \cd \paren{\truemeanf{\Predvar} - \truemeanf{\Predvar}}
@@ -33,8 +33,8 @@ By the law of iterated expectations (@thm-lie):
 
 $$
 \ba
-\E{\esterr{\truemeanf{\Predvar}}{\Outvar}\paren{\predfnf{\Predvar} - \truemeanf{\Predvar}}}
-&= \E{\E{\esterr{\truemeanf{\Predvar}}{\Outvar}\paren{\predfnf{\Predvar} - \truemeanf{\Predvar}} \mid \Predvar}}
+\E{\prederrf{\truemean}\paren{\predfnf{\Predvar} - \truemeanf{\Predvar}}}
+&= \E{\E{\prederrf{\truemean}\paren{\predfnf{\Predvar} - \truemeanf{\Predvar}} \mid \Predvar}}
 && \text{(law of iterated expectations)} \\
 &= \E{0}
 && \text{(the conditional expectation is } 0 \text{)} \\
@@ -52,7 +52,7 @@ $$
 
 In @exr-best-predictor, take the constant [prediction](#def-prediction) $\predfn_1\paren{\Predvar} = 3$.
 When $\Predvar = 0$, $\truemeanf{0} = 1$, so $\predfn_1\paren{0} - \truemeanf{0} = 2$,
-and $\esterr{\truemeanf{\Predvar}}{\Outvar} = 1 - \Outvar$ is $1$ or $-1$ with equal [probability](#def-probability),
+and $\prederrf{\truemean} = 1 - \Outvar$ is $1$ or $-1$ with equal [probability](#def-probability),
 so the product has conditional mean $0$.
 The same cancellation happens when $\Predvar = 1$,
 so the expectation of the product is $0$.

_subfiles/_lem-prediction-error-split.qmd

@@ -5,21 +5,21 @@ Let $\truemeanf{\Predvar} \eqdef \E{\Outvar \mid \Predvar}$ be the [conditional
 For any [prediction function](#def-prediction) $\predfnf{\Predvar}$,
 the [prediction error](#def-prediction-error) splits as:
 
-$$\esterr{\predfnf{\Predvar}}{\Outvar} = \esterr{\truemeanf{\Predvar}}{\Outvar} + \paren{\predfnf{\Predvar} - \truemeanf{\Predvar}}$$
+$$\prederrf{\predfn} = \prederrf{\truemean} + \paren{\predfnf{\Predvar} - \truemeanf{\Predvar}}$$
 
 :::
 
 ::: proof
 
 $$
 \ba
-\esterr{\predfnf{\Predvar}}{\Outvar}
+\prederrf{\predfn}
 &= \predfnf{\Predvar} - \Outvar
-&& \text{(definition of } \esterr{\predfnf{\Predvar}}{\Outvar} \text{)} \\
+&& \text{(definition of } \prederrf{\predfn} \text{)} \\
 &= \paren{\truemeanf{\Predvar} - \Outvar} + \paren{\predfnf{\Predvar} - \truemeanf{\Predvar}}
 && \text{(add and subtract } \truemeanf{\Predvar} \text{)} \\
-&= \esterr{\truemeanf{\Predvar}}{\Outvar} + \paren{\predfnf{\Predvar} - \truemeanf{\Predvar}}
-&& \text{(definition of } \esterr{\truemeanf{\Predvar}}{\Outvar} \text{)}
+&= \prederrf{\truemean} + \paren{\predfnf{\Predvar} - \truemeanf{\Predvar}}
+&& \text{(definition of } \prederrf{\truemean} \text{)}
 \ea
 $$
 
@@ -32,9 +32,9 @@ $$
 
 In @exr-best-predictor,
 when $\Predvar = 0$ and $\Outvar = 0$,
-the constant [prediction](#def-prediction) $\predfn_1\paren{\Predvar} = 3$ has [prediction error](#def-prediction-error) $\esterr{\predfn_1\paren{\Predvar}}{\Outvar} = 3$.
+the constant [prediction](#def-prediction) $\predfn_1\paren{\Predvar} = 3$ has [prediction error](#def-prediction-error) $\prederrf{\predfn_1} = 3$.
 The conditional mean is $\truemeanf{0} = 1$,
-so $\esterr{\truemeanf{\Predvar}}{\Outvar} = 1$ and $\predfn_1\paren{0} - \truemeanf{0} = 2$,
+so $\prederrf{\truemean} = 1$ and $\predfn_1\paren{0} - \truemeanf{0} = 2$,
 and $3 = 1 + 2$.
 
 :::

_subfiles/_thm-risk-decomposition.qmd

@@ -19,15 +19,20 @@ and @thm-linearity-expectation:
 $$
 \ba
 \popriskf{\predfn}
-&= \E{\sqf{\esterr{\predfnf{\Predvar}}{\Outvar}}}
+&= \E{\sqf{\prederrf{\predfn}}}
 && \text{(definition of the squared-error risk)} \\
-&= \E{\sqf{\esterr{\truemeanf{\Predvar}}{\Outvar} + \paren{\predfnf{\Predvar} - \truemeanf{\Predvar}}}}
+&= \E{\sqf{\prederrf{\truemean} + \devof{\predfnf{\Predvar}}{\truemeanf{\Predvar}}}}
 && \text{(the prediction error splits at } \truemean \text{)} \\
-&= \E{\sqf{\esterr{\truemeanf{\Predvar}}{\Outvar}}} + 2 \cd \E{\esterr{\truemeanf{\Predvar}}{\Outvar}\paren{\predfnf{\Predvar} - \truemeanf{\Predvar}}} + \E{\sqf{\predfnf{\Predvar} - \truemeanf{\Predvar}}}
+&= \E{\sqf{\prederrf{\truemean}}}
++ 2 \cd \E{\prederrf{\truemean} \cd \devof{\predfnf{\Predvar}}{\truemeanf{\Predvar}}}
++ \E{\sqf{\devof{\predfnf{\Predvar}}{\truemeanf{\Predvar}}}}
 && \text{(expand the square; linearity of expectation)} \\
-&= \E{\sqf{\esterr{\truemeanf{\Predvar}}{\Outvar}}} + 2 \cd 0 + \E{\sqf{\predfnf{\Predvar} - \truemeanf{\Predvar}}}
+&= \E{\sqf{\prederrf{\truemean}}}
++ 2 \cd 0
++ \E{\sqf{\devof{\predfnf{\Predvar}}{\truemeanf{\Predvar}}}}
 && \text{(the cross term is } 0 \text{)} \\
-&= \popriskf{\truemean} + \E{\sqf{\predfnf{\Predvar} - \truemeanf{\Predvar}}}
+&= \popriskf{\truemean}
++ \E{\sqf{\devof{\predfnf{\Predvar}}{\truemeanf{\Predvar}}}}
 && \text{(definition of the squared-error risk of } \truemean \text{)}
 \ea
 $$