Upperbounding the expected value of an L2-norm difference
I am trying to find an upperbound for $$E_Ileft[sum_{k=I}^n a_k^2 - sum_{k=I}^n b_k^2right],$$ where the expectation is taken over the random variable $I$. The tuples $a$ and $b$ are real and $I$ may take values on ${1,...,n}$.
I checked Jensen's inequalites but without success. Any help would be appreciated.
probability inequality norm jensen-inequality
asked Nov 26 '18 at 19:04
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add a comment |
I am trying to find an upperbound for $$E_Ileft[sum_{k=I}^n a_k^2 - sum_{k=I}^n b_k^2right],$$ where the expectation is taken over the random variable $I$. The tuples $a$ and $b$ are real and $I$ may take values on ${1,...,n}$.
I checked Jensen's inequalites but without success. Any help would be appreciated.
probability inequality norm jensen-inequality
asked Nov 26 '18 at 19:04
Embid
1
What is the relation between $a_k, b_k$ and $I$?
– herb steinberg
Nov 26 '18 at 22:50
Assuming you seek a bound on the expectation of a random length sum of fixed real numbers, clearly $||a||_2^2=sum_{k=1}^n a_k^2$ is an upper bound.
– Macavity
Nov 27 '18 at 1:29
add a comment |
I am trying to find an upperbound for $$E_Ileft[sum_{k=I}^n a_k^2 - sum_{k=I}^n b_k^2right],$$ where the expectation is taken over the random variable $I$. The tuples $a$ and $b$ are real and $I$ may take values on ${1,...,n}$.
I checked Jensen's inequalites but without success. Any help would be appreciated.
probability inequality norm jensen-inequality
asked Nov 26 '18 at 19:04
Embid
1
I am trying to find an upperbound for $$E_Ileft[sum_{k=I}^n a_k^2 - sum_{k=I}^n b_k^2right],$$ where the expectation is taken over the random variable $I$. The tuples $a$ and $b$ are real and $I$ may take values on ${1,...,n}$.
I checked Jensen's inequalites but without success. Any help would be appreciated.
probability inequality norm jensen-inequality
probability inequality norm jensen-inequality
asked Nov 26 '18 at 19:04
Embid
1
asked Nov 26 '18 at 19:04
Embid
1
asked Nov 26 '18 at 19:04
Embid
1
asked Nov 26 '18 at 19:04
Embid
1
asked Nov 26 '18 at 19:04
Embid
1
1
What is the relation between $a_k, b_k$ and $I$?
– herb steinberg
Nov 26 '18 at 22:50
Assuming you seek a bound on the expectation of a random length sum of fixed real numbers, clearly $||a||_2^2=sum_{k=1}^n a_k^2$ is an upper bound.
– Macavity
Nov 27 '18 at 1:29
add a comment |
What is the relation between $a_k, b_k$ and $I$?
– herb steinberg
Nov 26 '18 at 22:50
Assuming you seek a bound on the expectation of a random length sum of fixed real numbers, clearly $||a||_2^2=sum_{k=1}^n a_k^2$ is an upper bound.
– Macavity
Nov 27 '18 at 1:29
What is the relation between $a_k, b_k$ and $I$?
– herb steinberg
Nov 26 '18 at 22:50
What is the relation between $a_k, b_k$ and $I$?
– herb steinberg
Nov 26 '18 at 22:50
Assuming you seek a bound on the expectation of a random length sum of fixed real numbers, clearly $||a||_2^2=sum_{k=1}^n a_k^2$ is an upper bound.
– Macavity
Nov 27 '18 at 1:29
Assuming you seek a bound on the expectation of a random length sum of fixed real numbers, clearly $||a||_2^2=sum_{k=1}^n a_k^2$ is an upper bound.
– Macavity
Nov 27 '18 at 1:29
add a comment |
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What is the relation between $a_k, b_k$ and $I$?
– herb steinberg
Nov 26 '18 at 22:50
Assuming you seek a bound on the expectation of a random length sum of fixed real numbers, clearly $||a||_2^2=sum_{k=1}^n a_k^2$ is an upper bound.
– Macavity
Nov 27 '18 at 1:29