Is there a concentration inequality for the rectified gaussian distribution? For example, let $u_i$, $i=1,...,n$ be a sequence of i.i.d. standard normal random variables. Is it possible to bound $P\left\{\left\vert n^{-1}\sum_{i=1}^n \max\{0,\,u_i\}-\mathbb E\left[n^{-1}\sum_{i=1}^n \max\{0,\,u_i\}\right]\right\vert\leq t\right\}$ for any $t\geq 0$?
2026-02-23 06:21:49.1771827709
Tail bounds for sum of rectified gaussian variables
147 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in PROBABILITY-DISTRIBUTIONS
- Given is $2$ dimensional random variable $(X,Y)$ with table. Determine the correlation between $X$ and $Y$
- Statistics based on empirical distribution
- Given $U,V \sim R(0,1)$. Determine covariance between $X = UV$ and $V$
- Comparing Exponentials of different rates
- Linear transform of jointly distributed exponential random variables, how to identify domain?
- Closed form of integration
- Given $X$ Poisson, and $f_{Y}(y\mid X = x)$, find $\mathbb{E}[X\mid Y]$
- weak limit similiar to central limit theorem
- Probability question: two doors, select the correct door to win money, find expected earning
- Calculating $\text{Pr}(X_1<X_2)$
Related Questions in DISTRIBUTION-TAILS
- Tail Value at Risk of Normal Distribution
- Probability that an infinite sequence of i.i.d. integers has a repetition
- Is there a way to lower bound the left tail probability of a random variable?
- Applying Chernoff's/Hoeffding's Tail Bounds for Bounded, Dependent Variables
- To establish an inequality using Chebyshev's probability bound
- Heavy tailed distributions and their sum
- An explicit expression for tail probability using fourier transform
- Comparing two sum of fractal moments for heavy-tail distribution
- A classical result of first hitting time of simple random walk 1
- Value at Risk: Coherent risk measure for normal distribution
Related Questions in GAUSSIAN
- How to fit a Gaussian approximation to the likelihood curve at maximum?
- How can I find percentile $P_{10}$ and $P_{90}$ for Normal Distribution with Mean as $100$ and Standard Deviation as $3$?
- Give probability space $(\Omega,F,\mathbb P)$ & random variable $X:\Omega \to \mathbb R$ on $(\Omega,F,\mathbb P)$ so $X$ has normal distribution.
- Analyticity of determinant formula for Gaussian integral
- Searching for a second order ODE whose solution is bell shape (Gaussian function)
- Expectation: sigmoid times mixture of Gaussians
- Joint Gaussian distribution implies Gaussian + independence?
- how was the gaussian distribution developed? (question of an answer already done)
- A uniform distributed random vector on euclidean ball is sub gaussian
- Predictive distribution of SPGP
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?