Integral of Huber piecewise function.
$begingroup$
The below $psi$-fuction is the derivetive of Huber function, how can we find the integral of it? the answer is given. Can anybody prove it.][1]
$$
psi(u_i) =
[
begin{cases}
u_i & |u_i|leq c \
0 & |u_i|> c
end{cases}
]
$$
$$
sigma^2_psi = int_{-c}^{c} psi^2(u_i). d F(u_i),
$$
where $$
dF(u_i) = frac{1}{sqrt{2pi}} . e^-{frac{u_i^2}{2}}$$
the quastion is how can we prove that
prove that
$$
sigma^2_psi = I(|u_i| leq c) psi^2(u_i)$$
calculus integration robust-statistics
edited Dec 5 '18 at 9:37
Bernard
119k639112
asked Dec 5 '18 at 7:38
atiq marwatatiq marwat
11
$endgroup$
add a comment |
$begingroup$
The below $psi$-fuction is the derivetive of Huber function, how can we find the integral of it? the answer is given. Can anybody prove it.][1]
$$
psi(u_i) =
[
begin{cases}
u_i & |u_i|leq c \
0 & |u_i|> c
end{cases}
]
$$
$$
sigma^2_psi = int_{-c}^{c} psi^2(u_i). d F(u_i),
$$
where $$
dF(u_i) = frac{1}{sqrt{2pi}} . e^-{frac{u_i^2}{2}}$$
the quastion is how can we prove that
prove that
$$
sigma^2_psi = I(|u_i| leq c) psi^2(u_i)$$
calculus integration robust-statistics
edited Dec 5 '18 at 9:37
Bernard
119k639112
asked Dec 5 '18 at 7:38
atiq marwatatiq marwat
11
$endgroup$
$begingroup$
Can you be more precise with what it is you are trying to prove? It appears that your right hand side is a non-constant function of $u_i,$ but the left hand side is a constant.
$endgroup$
– Katie Dobbs
Dec 5 '18 at 16:23
add a comment |
$begingroup$
The below $psi$-fuction is the derivetive of Huber function, how can we find the integral of it? the answer is given. Can anybody prove it.][1]
$$
psi(u_i) =
[
begin{cases}
u_i & |u_i|leq c \
0 & |u_i|> c
end{cases}
]
$$
$$
sigma^2_psi = int_{-c}^{c} psi^2(u_i). d F(u_i),
$$
where $$
dF(u_i) = frac{1}{sqrt{2pi}} . e^-{frac{u_i^2}{2}}$$
the quastion is how can we prove that
prove that
$$
sigma^2_psi = I(|u_i| leq c) psi^2(u_i)$$
calculus integration robust-statistics
edited Dec 5 '18 at 9:37
Bernard
119k639112
asked Dec 5 '18 at 7:38
atiq marwatatiq marwat
11
$endgroup$
The below $psi$-fuction is the derivetive of Huber function, how can we find the integral of it? the answer is given. Can anybody prove it.][1]
$$
psi(u_i) =
[
begin{cases}
u_i & |u_i|leq c \
0 & |u_i|> c
end{cases}
]
$$
$$
sigma^2_psi = int_{-c}^{c} psi^2(u_i). d F(u_i),
$$
where $$
dF(u_i) = frac{1}{sqrt{2pi}} . e^-{frac{u_i^2}{2}}$$
the quastion is how can we prove that
prove that
$$
sigma^2_psi = I(|u_i| leq c) psi^2(u_i)$$
calculus integration robust-statistics
calculus integration robust-statistics
edited Dec 5 '18 at 9:37
Bernard
119k639112
asked Dec 5 '18 at 7:38
atiq marwatatiq marwat
11
edited Dec 5 '18 at 9:37
Bernard
119k639112
asked Dec 5 '18 at 7:38
atiq marwatatiq marwat
11
edited Dec 5 '18 at 9:37
Bernard
119k639112
edited Dec 5 '18 at 9:37
Bernard
119k639112
edited Dec 5 '18 at 9:37
Bernard
119k639112
119k639112
asked Dec 5 '18 at 7:38
atiq marwatatiq marwat
11
asked Dec 5 '18 at 7:38
atiq marwatatiq marwat
11
asked Dec 5 '18 at 7:38
atiq marwatatiq marwat
11
11
$begingroup$
Can you be more precise with what it is you are trying to prove? It appears that your right hand side is a non-constant function of $u_i,$ but the left hand side is a constant.
$endgroup$
– Katie Dobbs
Dec 5 '18 at 16:23
add a comment |
$begingroup$
Can you be more precise with what it is you are trying to prove? It appears that your right hand side is a non-constant function of $u_i,$ but the left hand side is a constant.
$endgroup$
– Katie Dobbs
Dec 5 '18 at 16:23
$begingroup$
Can you be more precise with what it is you are trying to prove? It appears that your right hand side is a non-constant function of $u_i,$ but the left hand side is a constant.
$endgroup$
– Katie Dobbs
Dec 5 '18 at 16:23
$begingroup$
Can you be more precise with what it is you are trying to prove? It appears that your right hand side is a non-constant function of $u_i,$ but the left hand side is a constant.
$endgroup$
– Katie Dobbs
Dec 5 '18 at 16:23
add a comment |
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$begingroup$
Can you be more precise with what it is you are trying to prove? It appears that your right hand side is a non-constant function of $u_i,$ but the left hand side is a constant.
$endgroup$
– Katie Dobbs
Dec 5 '18 at 16:23