All Questions
5 questions
1
vote
0
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Inequality involving random vectors and absolute values
Let $\mathbb{X}, \mathbb{Y} \subset \mathbb{R}^d$ be finite sets. Suppose random vectors $X \in \mathbb{X}$ and $Y \in \mathbb{Y}$ are sampled according to a joint distribution $\mathbb{P}_{XY}$. ...
2
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2
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632
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An alternative proof of Bayesian Cramer-Rao
My question is:
Are there an alternative proof of Cramer-Rao lower bound that does not use
Cauchy-Swartz inequality?
Let me outline the classical proof and explain why I am interested in this ...
3
votes
1
answer
3k
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Is there a tight lower bound for the expectation of the product of two positive valued random variables?
Let $X,Y$ be two (dependent) random variables with $\mathbb{P}(X\ge 0)=\mathbb{P}(Y\ge 0)=1$.
I want to find a tight lower bound of $\mathbb{E}(XY)$ when $X,Y$ are non-negative, almost surely.
...
CommunityBot
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2
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0
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58
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Bounds for $\sum_{t=1}^Tn_t(s_t)^{-\alpha}\mu(s_t)$ where $n_t(s) = \sum_{1 \le t' \le t} 1_{\{s_{t'}=s\}}$ for $s \in [k]$ and $\mu \in \Delta_k$
Disclaimer: I'm not certain this is the right venue for this post, but I'll give it a try...
So trying prove some bounds in my ongoing work in theoretical reinforcement learning, I encountered the ...
- 6,853
12
votes
3
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549
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A probabilistic angle inequality
Conjecture: There is a universal constant $c$ such that for any fixed nonzero real vector $q$ of any dimension $n$ and any random vector $p$ of the same dimension $n$ with independent components ...
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