Perturbation of Rademacher average
$begingroup$
Given a set of vectors, $Asubset R^n$, we define
$R(A) = frac{1}{N} mathbb{E}_sigma left[ sup_{ain A} sum_{i=1}^Nsigma_i a_iright]$,
where $sigma$ is Rademacher random variable such that $P(sigma=1) =P(sigma =-1) =frac{1}{2}$. Also, define
$tilde{R}(A) = frac{1}{N} mathbb{E}_sigma left[ sup_{ain A} betasigma_1a_1+sum_{i=2}^Nsigma_i a_iright]$,
where $beta ge 1$. If we further assume that for any $ain A$, we also have $-a in A$. Then, I was wondering, if we can prove
$tilde{R}(A) ge R(A)$?
Thanks!
probability probability-theory rademacher-distribution
asked Jan 16 at 23:42
user3138073user3138073
1758
$endgroup$
add a comment |
$begingroup$
Given a set of vectors, $Asubset R^n$, we define
$R(A) = frac{1}{N} mathbb{E}_sigma left[ sup_{ain A} sum_{i=1}^Nsigma_i a_iright]$,
where $sigma$ is Rademacher random variable such that $P(sigma=1) =P(sigma =-1) =frac{1}{2}$. Also, define
$tilde{R}(A) = frac{1}{N} mathbb{E}_sigma left[ sup_{ain A} betasigma_1a_1+sum_{i=2}^Nsigma_i a_iright]$,
where $beta ge 1$. If we further assume that for any $ain A$, we also have $-a in A$. Then, I was wondering, if we can prove
$tilde{R}(A) ge R(A)$?
Thanks!
probability probability-theory rademacher-distribution
asked Jan 16 at 23:42
user3138073user3138073
1758
$endgroup$
add a comment |
$begingroup$
Given a set of vectors, $Asubset R^n$, we define
$R(A) = frac{1}{N} mathbb{E}_sigma left[ sup_{ain A} sum_{i=1}^Nsigma_i a_iright]$,
where $sigma$ is Rademacher random variable such that $P(sigma=1) =P(sigma =-1) =frac{1}{2}$. Also, define
$tilde{R}(A) = frac{1}{N} mathbb{E}_sigma left[ sup_{ain A} betasigma_1a_1+sum_{i=2}^Nsigma_i a_iright]$,
where $beta ge 1$. If we further assume that for any $ain A$, we also have $-a in A$. Then, I was wondering, if we can prove
$tilde{R}(A) ge R(A)$?
Thanks!
probability probability-theory rademacher-distribution
asked Jan 16 at 23:42
user3138073user3138073
1758
$endgroup$
Given a set of vectors, $Asubset R^n$, we define
$R(A) = frac{1}{N} mathbb{E}_sigma left[ sup_{ain A} sum_{i=1}^Nsigma_i a_iright]$,
where $sigma$ is Rademacher random variable such that $P(sigma=1) =P(sigma =-1) =frac{1}{2}$. Also, define
$tilde{R}(A) = frac{1}{N} mathbb{E}_sigma left[ sup_{ain A} betasigma_1a_1+sum_{i=2}^Nsigma_i a_iright]$,
where $beta ge 1$. If we further assume that for any $ain A$, we also have $-a in A$. Then, I was wondering, if we can prove
$tilde{R}(A) ge R(A)$?
Thanks!
probability probability-theory rademacher-distribution
probability probability-theory rademacher-distribution
asked Jan 16 at 23:42
user3138073user3138073
1758
asked Jan 16 at 23:42
user3138073user3138073
1758
asked Jan 16 at 23:42
user3138073user3138073
1758
asked Jan 16 at 23:42
user3138073user3138073
1758
asked Jan 16 at 23:42
user3138073user3138073
1758
1758
add a comment |
add a comment |
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