New answers tagged expectation
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Proving bound on expectation of likelihood ratio involving mixtures
I am now trying to show that $H(\mu) \leq 1$ for $|\mu| \geq c$. As $H$ is an even function, it is sufficient to show that $H(\mu) \leq 1$ for $\mu \geq c$.
This is not true. E.g., suppose that $c=1$ ...
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Upper Bound for $\mathbb{E}\left[\max_{j \in \mathcal{N}} h_{j}\right]$
For an alternative bound (which I just saw was referred to by Sandeep in the comments while revising this), you can adapt the standard argument for the expectation of the maximum of Gaussians.
I do ...
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Upper Bound for $\mathbb{E}\left[\max_{j \in \mathcal{N}} h_{j}\right]$
$\newcommand\si\sigma$The inequality in question fails to hold if e.g. $\mathcal N=[n]:=\{1,\dots,n\}$, the $h_j$'s are i.i.d. exponential random variables, and $n=4$. This follows because then
$$E\...
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Upper Bound for $\mathbb{E}\left[\max_{j \in \mathcal{N}} h_{j}\right]$
For $\{H_j\}_{j∈N}$ independent Gamma random variables as $H_j > 0$ then $max_{j\in N} H_j \leq \sum_{j\in N} H_j$. As $H$ are independent then $$\mathbb{E}[max_{j\in N} H_j] \leq \sum_{j\in N} \...
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