Lower bound for Expected Value of Euclidean Norm
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If $boldsymbolxsimmathcalN(0,boldsymbolI_n)$, then the expected value of the Euclidean norm has the following lower bound:
$$
mathbbE[|boldsymbolx|_2]=mathbbEleft[sqrtboldsymbolx^Tboldsymbolxright]geqsqrtn(1-o(1)).
$$
I was wondering how to get this lower bound. In the book I have read, the author mentioned that the lower bound can be obtained via the concentration inequality of chi-square random variable.
Thank you in advance.
probability
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If $boldsymbolxsimmathcalN(0,boldsymbolI_n)$, then the expected value of the Euclidean norm has the following lower bound:
$$
mathbbE[|boldsymbolx|_2]=mathbbEleft[sqrtboldsymbolx^Tboldsymbolxright]geqsqrtn(1-o(1)).
$$
I was wondering how to get this lower bound. In the book I have read, the author mentioned that the lower bound can be obtained via the concentration inequality of chi-square random variable.
Thank you in advance.
probability
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
If $boldsymbolxsimmathcalN(0,boldsymbolI_n)$, then the expected value of the Euclidean norm has the following lower bound:
$$
mathbbE[|boldsymbolx|_2]=mathbbEleft[sqrtboldsymbolx^Tboldsymbolxright]geqsqrtn(1-o(1)).
$$
I was wondering how to get this lower bound. In the book I have read, the author mentioned that the lower bound can be obtained via the concentration inequality of chi-square random variable.
Thank you in advance.
probability
If $boldsymbolxsimmathcalN(0,boldsymbolI_n)$, then the expected value of the Euclidean norm has the following lower bound:
$$
mathbbE[|boldsymbolx|_2]=mathbbEleft[sqrtboldsymbolx^Tboldsymbolxright]geqsqrtn(1-o(1)).
$$
I was wondering how to get this lower bound. In the book I have read, the author mentioned that the lower bound can be obtained via the concentration inequality of chi-square random variable.
Thank you in advance.
probability
asked Aug 17 at 2:54
M.Shen
263
263
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