Concentration inequality for median
$xi_1,xi_2,ldots,xi_n$ are iid sub-Gaussian random variables (i.e, $P(xi_1>t)leq e^{-t^2/2}$ for $t>0$) with mean $0$ and $a_1,a_2,ldots,a_ninmathbb{R}$.
Define $a_0:= lim_{deltadownarrow 0}argmin frac1nsum_{k=1}^n |a -a_k|+delta a^2$ and $X_0:= lim_{deltadownarrow 0}argmin frac1nsum_{k=1}^n |x -X_k|+delta x^2$ where $X_k:= a_k+xi_k.$ What is an appropriate upper bound for $P(|X_0-a_0|>t)?$
I have tried doing that using McDiarmid type inequality for sub-Gaussian but the concentration inequality is for $P(|X_0-EX_0|>t)$ in that case. Any help would be appreciated.
probability concentration-of-measure
asked 2 days ago
John_Wick
1,401111
add a comment |
$xi_1,xi_2,ldots,xi_n$ are iid sub-Gaussian random variables (i.e, $P(xi_1>t)leq e^{-t^2/2}$ for $t>0$) with mean $0$ and $a_1,a_2,ldots,a_ninmathbb{R}$.
Define $a_0:= lim_{deltadownarrow 0}argmin frac1nsum_{k=1}^n |a -a_k|+delta a^2$ and $X_0:= lim_{deltadownarrow 0}argmin frac1nsum_{k=1}^n |x -X_k|+delta x^2$ where $X_k:= a_k+xi_k.$ What is an appropriate upper bound for $P(|X_0-a_0|>t)?$
I have tried doing that using McDiarmid type inequality for sub-Gaussian but the concentration inequality is for $P(|X_0-EX_0|>t)$ in that case. Any help would be appreciated.
probability concentration-of-measure
asked 2 days ago
John_Wick
1,401111
add a comment |
$xi_1,xi_2,ldots,xi_n$ are iid sub-Gaussian random variables (i.e, $P(xi_1>t)leq e^{-t^2/2}$ for $t>0$) with mean $0$ and $a_1,a_2,ldots,a_ninmathbb{R}$.
Define $a_0:= lim_{deltadownarrow 0}argmin frac1nsum_{k=1}^n |a -a_k|+delta a^2$ and $X_0:= lim_{deltadownarrow 0}argmin frac1nsum_{k=1}^n |x -X_k|+delta x^2$ where $X_k:= a_k+xi_k.$ What is an appropriate upper bound for $P(|X_0-a_0|>t)?$
I have tried doing that using McDiarmid type inequality for sub-Gaussian but the concentration inequality is for $P(|X_0-EX_0|>t)$ in that case. Any help would be appreciated.
probability concentration-of-measure
asked 2 days ago
John_Wick
1,401111
$xi_1,xi_2,ldots,xi_n$ are iid sub-Gaussian random variables (i.e, $P(xi_1>t)leq e^{-t^2/2}$ for $t>0$) with mean $0$ and $a_1,a_2,ldots,a_ninmathbb{R}$.
Define $a_0:= lim_{deltadownarrow 0}argmin frac1nsum_{k=1}^n |a -a_k|+delta a^2$ and $X_0:= lim_{deltadownarrow 0}argmin frac1nsum_{k=1}^n |x -X_k|+delta x^2$ where $X_k:= a_k+xi_k.$ What is an appropriate upper bound for $P(|X_0-a_0|>t)?$
I have tried doing that using McDiarmid type inequality for sub-Gaussian but the concentration inequality is for $P(|X_0-EX_0|>t)$ in that case. Any help would be appreciated.
probability concentration-of-measure
probability concentration-of-measure
asked 2 days ago
John_Wick
1,401111
asked 2 days ago
John_Wick
1,401111
asked 2 days ago
John_Wick
1,401111
asked 2 days ago
John_Wick
1,401111
asked 2 days ago
John_Wick
1,401111
1,401111
add a comment |
add a comment |
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