Questions tagged [tail-bound]

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Probability bound on Maxima under random sampling

I have a set $S$ = {$e_1,e_2,..e_{400}$} of 400 elements and a non-linear function $f:2^{(S)}\to[0,1]$ that takes a subset of $S$ and returns a real number in $[0,1]$. I want to compute the subset for ...
CSStudent's user avatar
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2 votes
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For random variable $Z=\max_i X_i$, can we bound $\mathbb{E}(Z|Z>\tau)$ with $\mathbb{E}(Z)$

Let $X_1,…,X_n$ be independent, but not necessarily identical, non-negative random variables. Let $Z=\max_i(X_i)$. Fix a real $\tau > 0$. Is there a way to lower bound $$\mathbb{E}(Z|Z>\tau) >...
AspiringMat's user avatar
5 votes
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How to construct a confidence interval for the coefficients of a multivariate regression with dependence between dependent variables?

Suppose we have two linear regression models $y_1=a+bx+\epsilon_1$ where $\mathbb[\epsilon_1]=\sigma_1$ and $y_2=c+dx+\epsilon_2$ where $\mathbb[\epsilon_2]=\sigma_2$. In other words, I am using the ...
Amin's user avatar
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Bound on the expectation of a function of random variable having a strictly log-concave probability density

let $\theta \in \mathbb{R}^d$ be a random variable having a strictly log-concave probability density function, i.e \begin{equation} p(\theta) = e^{-\phi(\theta)} \end{equation} where $\phi(\theta)$ is ...
zsheeba's user avatar
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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 ...
Carl's user avatar
  • 1,166
1 vote
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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....
Carl's user avatar
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2 votes
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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&...
Charles's user avatar
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2 votes
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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 ...
Jakub Koubele's user avatar