Bound on an indefinite integral in kernel density estimation The 2019 Stack Overflow Developer Survey Results Are In Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Indefinite integralIndefinite IntegralIndefinite Integral of a functionFind the indefinite integralTricky Indefinite IntegralSolving an indefinite integralExplicit behavior of a sequence of integralsIndefinite integral checksBounding $frac(n^2 +log_5(n))cdot log_8(log_2(fracsqrtn2))2$ from above and belowIndefinite integral to find work
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Bound on an indefinite integral in kernel density estimation
The 2019 Stack Overflow Developer Survey Results Are In
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Indefinite integralIndefinite IntegralIndefinite Integral of a functionFind the indefinite integralTricky Indefinite IntegralSolving an indefinite integralExplicit behavior of a sequence of integralsIndefinite integral checksBounding $frac(n^2 +log_5(n))cdot log_8(log_2(fracsqrtn2))2$ from above and belowIndefinite integral to find work
$begingroup$
I am having trouble on what is probably a simple step in the proof of Theorem 24.1 in Asymptotic Statistics by Van der Vaart. Let $int K(y) dy = 1$. The author writes:
$$h^4 int K(y)y^2 dy int int_0^1 K(y)y^2 f''(x-shy)^2(1-s)^2dsdy$$
The integral of this with respect to $x$ is bounded above by:
$$h^4 Big( int K(y)y^2 dy Big)^2 int f''(x)^2 dx frac13$$
Does anyone know how to derive this bound?
indefinite-integrals upper-lower-bounds
asked Apr 6 at 21:03
John DoeJohn Doe
666
$endgroup$
add a comment |
$begingroup$
I am having trouble on what is probably a simple step in the proof of Theorem 24.1 in Asymptotic Statistics by Van der Vaart. Let $int K(y) dy = 1$. The author writes:
$$h^4 int K(y)y^2 dy int int_0^1 K(y)y^2 f''(x-shy)^2(1-s)^2dsdy$$
The integral of this with respect to $x$ is bounded above by:
$$h^4 Big( int K(y)y^2 dy Big)^2 int f''(x)^2 dx frac13$$
Does anyone know how to derive this bound?
indefinite-integrals upper-lower-bounds
asked Apr 6 at 21:03
John DoeJohn Doe
666
$endgroup$
add a comment |
$begingroup$
I am having trouble on what is probably a simple step in the proof of Theorem 24.1 in Asymptotic Statistics by Van der Vaart. Let $int K(y) dy = 1$. The author writes:
$$h^4 int K(y)y^2 dy int int_0^1 K(y)y^2 f''(x-shy)^2(1-s)^2dsdy$$
The integral of this with respect to $x$ is bounded above by:
$$h^4 Big( int K(y)y^2 dy Big)^2 int f''(x)^2 dx frac13$$
Does anyone know how to derive this bound?
indefinite-integrals upper-lower-bounds
asked Apr 6 at 21:03
John DoeJohn Doe
666
$endgroup$
I am having trouble on what is probably a simple step in the proof of Theorem 24.1 in Asymptotic Statistics by Van der Vaart. Let $int K(y) dy = 1$. The author writes:
$$h^4 int K(y)y^2 dy int int_0^1 K(y)y^2 f''(x-shy)^2(1-s)^2dsdy$$
The integral of this with respect to $x$ is bounded above by:
$$h^4 Big( int K(y)y^2 dy Big)^2 int f''(x)^2 dx frac13$$
Does anyone know how to derive this bound?
indefinite-integrals upper-lower-bounds
indefinite-integrals upper-lower-bounds
asked Apr 6 at 21:03
John DoeJohn Doe
666
asked Apr 6 at 21:03
John DoeJohn Doe
666
edited Apr 8 at 13:51
John Doe
asked Apr 6 at 21:03
John DoeJohn Doe
666
asked Apr 6 at 21:03
John DoeJohn Doe
666
asked Apr 6 at 21:03
John DoeJohn Doe
666
666
add a comment |
add a comment |
1 Answer
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Answer is located here: pg 25 https://repositorio.uniandes.edu.co/bitstream/handle/1992/20184/u672237.pdf?sequence=1&isAllowed=y
answered Apr 7 at 0:58
John DoeJohn Doe
666
$endgroup$
add a comment |
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$begingroup$
Answer is located here: pg 25 https://repositorio.uniandes.edu.co/bitstream/handle/1992/20184/u672237.pdf?sequence=1&isAllowed=y
answered Apr 7 at 0:58
John DoeJohn Doe
666
$endgroup$
add a comment |
$begingroup$
Answer is located here: pg 25 https://repositorio.uniandes.edu.co/bitstream/handle/1992/20184/u672237.pdf?sequence=1&isAllowed=y
answered Apr 7 at 0:58
John DoeJohn Doe
666
$endgroup$
add a comment |
$begingroup$
Answer is located here: pg 25 https://repositorio.uniandes.edu.co/bitstream/handle/1992/20184/u672237.pdf?sequence=1&isAllowed=y
answered Apr 7 at 0:58
John DoeJohn Doe
666
$endgroup$
Answer is located here: pg 25 https://repositorio.uniandes.edu.co/bitstream/handle/1992/20184/u672237.pdf?sequence=1&isAllowed=y
answered Apr 7 at 0:58
John DoeJohn Doe
666
answered Apr 7 at 0:58
John DoeJohn Doe
666
answered Apr 7 at 0:58
John DoeJohn Doe
666
answered Apr 7 at 0:58
John DoeJohn Doe
666
666
add a comment |
add a comment |
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