Getting Additive Relation from Multivariate Function: What Assumptions?
$begingroup$
Let's say I have a variable $p$ that is a function of two, possibly correlated, other random variables $a$ and $w$ per the function $f()$:
$p = f(w , a)$
What assumptions about $f$ would be necessary to arrive at the following relationship:
$w = g(p) - E[a | p]$,
where $g()$ is some unknown function and $E$ is the expectations operator. Or more generally, how could I write $w$ as the sum of some unknown function of $p$ and an unknown function of $a$.
For example, do I need to assume that $w$ and $a$ are additively separable in $f$ (i.e. $f(w,a) = f_w(w) + f_a(a)$)?
linear-algebra conditional-expectation
asked Jan 15 at 2:23
km5041km5041
12
$endgroup$
add a comment |
$begingroup$
Let's say I have a variable $p$ that is a function of two, possibly correlated, other random variables $a$ and $w$ per the function $f()$:
$p = f(w , a)$
What assumptions about $f$ would be necessary to arrive at the following relationship:
$w = g(p) - E[a | p]$,
where $g()$ is some unknown function and $E$ is the expectations operator. Or more generally, how could I write $w$ as the sum of some unknown function of $p$ and an unknown function of $a$.
For example, do I need to assume that $w$ and $a$ are additively separable in $f$ (i.e. $f(w,a) = f_w(w) + f_a(a)$)?
linear-algebra conditional-expectation
asked Jan 15 at 2:23
km5041km5041
12
$endgroup$
add a comment |
$begingroup$
Let's say I have a variable $p$ that is a function of two, possibly correlated, other random variables $a$ and $w$ per the function $f()$:
$p = f(w , a)$
What assumptions about $f$ would be necessary to arrive at the following relationship:
$w = g(p) - E[a | p]$,
where $g()$ is some unknown function and $E$ is the expectations operator. Or more generally, how could I write $w$ as the sum of some unknown function of $p$ and an unknown function of $a$.
For example, do I need to assume that $w$ and $a$ are additively separable in $f$ (i.e. $f(w,a) = f_w(w) + f_a(a)$)?
linear-algebra conditional-expectation
asked Jan 15 at 2:23
km5041km5041
12
$endgroup$
Let's say I have a variable $p$ that is a function of two, possibly correlated, other random variables $a$ and $w$ per the function $f()$:
$p = f(w , a)$
What assumptions about $f$ would be necessary to arrive at the following relationship:
$w = g(p) - E[a | p]$,
where $g()$ is some unknown function and $E$ is the expectations operator. Or more generally, how could I write $w$ as the sum of some unknown function of $p$ and an unknown function of $a$.
For example, do I need to assume that $w$ and $a$ are additively separable in $f$ (i.e. $f(w,a) = f_w(w) + f_a(a)$)?
linear-algebra conditional-expectation
linear-algebra conditional-expectation
asked Jan 15 at 2:23
km5041km5041
12
asked Jan 15 at 2:23
km5041km5041
12
asked Jan 15 at 2:23
km5041km5041
12
asked Jan 15 at 2:23
km5041km5041
12
asked Jan 15 at 2:23
km5041km5041
12
12
add a comment |
add a comment |
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