Related papers: Exact value for subgaussian norm of centered indic…
In this paper we consider Bayesian estimation for the parameters of inverse Gaussian distribution. Our emphasis is on Markov Chain Monte Carlo methods. We provide complete implementation of the Gibbs sampler algorithm. Assuming an…
In this short note we prove a maximal concentration lemma for sub-Gaussian random variables stating that for independent sub-Gaussian random variables we have \[P<(\max_{1\le i\le N}S_{i}>\epsilon>)…
For a skew normal random sequence, convergence rates of the distribution of its partial maximum to the Gumbel extreme value distribution are derived. The asymptotic expansion of the distribution of the normalized maximum is given under an…
In this expository note, we give a modern proof of Hanson-Wright inequality for quadratic forms in sub-gaussian random variables. We deduce a useful concentration inequality for sub-gaussian random vectors. Two examples are given to…
The target measure $\mu$ is the distribution of a random vector in a box $\cB$, a Cartesian product of bounded intervals. The Gibbs sampler is a Markov chain with invariant measure $\mu$. A ``coupling from the past'' construction of the…
We say that a random integer variable $X$ is monotone if the modulus of the characteristic function of $X$ is decreasing on $[0,\pi]$. This is the case for many commonly encountered variables, e.g., Bernoulli, Poisson and geometric random…
We find the exponential exact two-terms non-asymptotic expression for the maximum and minimum distribution of a non-Gaussian, in general case, random vector.
The goal of this note is to present a modification of the popular median of means estimator that achieves sub-Gaussian deviation bounds with nearly optimal constants under minimal assumptions on the underlying distribution. We build on a…
We prove that the tail probabilities of sums of independent uniform random variables, up to a multiplicative constant, are dominated by the Gaussian tail with matching variance and find the sharp constant for such stochastic domination.
In this paper we first provide a method to compute confidence intervals for the center of a piecewise normal distribution given a sample from this distribution, under certain assumptions. We then extend this method to an asymptotic setting,…
We suggest approximating the distribution of the sum of independent and identically distributed random variables with a Pareto-like tail by combining extreme value approximations for the largest summands with a normal approximation for the…
Gaussian-Bernoulli restricted Boltzmann machines (GBRBMs) are often used for semi-supervised anomaly detection, where they are trained using only normal data points. In GBRBM-based anomaly detection, normal and anomalous data are classified…
An algorithm is presented that, taking a sequence of independent Bernoulli random variables with parameter $1/2$ as inputs and using only rational arithmetic, simulates a Bernoulli random variable with possibly irrational parameter $\tau$.…
We investigate the convergence of series of random variables with second exponential moments. We give sufficient conditions for the convergence of these series with respect to an exponential Orlicz norm and almost surely. Applying this…
The standard textbook method for estimating the probability of a biased coin from finite tosses implicitly assumes the sample sizes are large and gives incorrect results for small samples. We describe the exact solution, which is correct…
Self-normalized processes arise naturally in many learning-related tasks. While self-normalized concentration has been extensively studied for scalar-valued processes, there are few results for multidimensional processes outside of the…
We investigate the problem of characterizing the optimal variance proxy for sub-Gaussian random variables,whose moment-generating function exhibits bounded growth at infinity. We apply a general characterization method to discrete random…
We study polynomial time algorithms for estimating the mean of a heavy-tailed multivariate random vector. We assume only that the random vector $X$ has finite mean and covariance. In this setting, the radius of confidence intervals achieved…
Estimates are constructed for the deviation of the concentration functions of sums of independent random variables with finite variances from the folded normal distribution function without any assumptions concerning the existence of the…
We deduce in this paper the sufficient conditions for weak convergence of centered and normed deviation of the u-statistics with values in the space of the real valued continuous function defined on some compact metric space. We obtain also…