Questions tagged [tail-bound]

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Tight "uniform" tail bounds on binomial distribution

I am interested in upper bounds on the probability $P\left[\frac{X}{n} <p-\delta\right]$ for a binomially distributed random variable $X\sim B(n,p)$, which are both (1) as tight as reasonably ...
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Does Cramer's condition imply strong mixing?

In Theorem 1.4 of D. Bosq the Cramer's condition is a prerequisite for the tail bound of sum of dependent variables. The Theorem is as follows: Let $(X_t,t\in\mathbb{Z})$ be a zero-mean real-valued ...
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How to bound sub-exponential variables?

I am trying to understand bounding sub-exponential variables. Suppose for $t=2,\cdots,n$, we have \begin{equation} u_{t-1}u_t \end{equation} where $u_t$ and $u_{t-1}$ are sub-Gaussian. We know that ...
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Lower bounding the sum of product of two sub-Gaussian variables where one follows an AR(1) process

Suppose we have the sum \begin{equation} \sum_{t=2}^{n}\epsilon_{t-1}u_t \end{equation} where $\epsilon_t$ and $u_t$ are both sub-Gaussian variables. Further suppose that while $u_2,\cdots,u_n$ are i....
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A front-loaded Gumbel-like distribution

I'm looking for a distribution that is somewhat like the Gumbel distribution and I was wondering if anyone could help. The parameters are a positive integer $n$ and real numbers $\mu>0$ and $\sigma&...
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Bounding the tail of sum of discrete distributions (via sub-gaussianity)

I have the following problem: we have a sequence of random variables $Z_1, ..., Z_n$ which are summed up; let's denote $X$ to be their sum. We observe a number $\epsilon$ that is sampled from $X$ and ...
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