相关论文: A note on optimal probability lower bounds for cen…

In this paper, we obtain a $p$-th moment bound for the suprema of a log-concave-tailed nonhomogeneous chaos process, which is optimal in some special cases. A crucial ingredient of the proof is a novel decoupling inequality, which may be of…

This paper investigates and bounds the expected solution quality of combinatorial optimization problems when feasible solutions are chosen at random. Loose general bounds are discovered, as well as families of combinatorial optimization…

This paper provides a finite sample bound for the error term in the Edgeworth expansion for a sum of independent, potentially discrete, nonlattice random vectors, using a uniform-in-$P$ version of the weaker Cram\'{e}r condition in Angst…

Let $(\xi_i)_{i=1,...,n}$ be a sequence of independent and symmetric random variables. We consider the upper bounds on tail probabilities of self-normalized deviations $$ \mathbf{P} \Big( \max_{1\leq k \leq n} \sum_{i=1}^{k} |\xi_i|\big/…

In this paper we consider the inference rules of System P in the framework of coherent imprecise probabilistic assessments. Exploiting our algorithms, we propagate the lower and upper probability bounds associated with the conditional…

The center of gravity is one of the most frequently used algorithm for position reconstruction with different analytical forms for the noise optimization. The error distributions of the different forms are essential instruments to improve…

For arbitrary two probability measures on real d-space with given means and variances (covariance matrices), we provide lower bounds for their total variation distance. In the one-dimensional case, a tight bound is given.

Let $X$ be a random variable and define its concentration function by $$\mathcal{Q}_{h}(X)=\sup_{x\in \mathbb{R}}\mathbb{P}(X\in (x,x+h]).$$ For a sum $S_n=X_1+\cdots+X_n$ of independent real-valued random variables the Kolmogorov-Rogozin…

For a random walk in an elliptic i.i.d. random environment in dimension greater than or equal to 4, satisfying the a ballisticity condition slightly weaker than condition (T'), We consider the probability of linear slowdown. We show an…

For the optimal success probability under minimum-error discrimination between $r\geq2$ arbitrary quantum states prepared with any a priori probabilities, we find new general analytical lower and upper bounds and specify the relations…

Let $A$ be an $n\times n$ random matrix with i.i.d. entries of zero mean, unit variance and a bounded subgaussian moment. We show that the condition number $s_{\max}(A)/s_{\min}(A)$ satisfies the small ball probability estimate $${\mathbb…

Given a set of independent Poisson random variables with common mean, we study the distribution of their maximum and obtain an accurate asymptotic formula to locate the most probable value of the maximum. We verify our analytic results with…

A central computational problem for analyzing and model checking various classes of infinite-state recursive probabilistic systems (including quasi-birth-death processes, multi-type branching processes, stochastic context-free grammars,…

This paper proves, in very general settings, that convex risk minimization is a procedure to select a unique conditional probability model determined by the classification problem. Unlike most previous work, we give results that are general…

Real numbers from the interval [0, 1] are randomly selected with uniform distribution. There are $n$ of them and they are revealed one by one. However, we do not know their values but only their relative ranks. We want to stop on recently…

We consider the problem of estimating confidence intervals for the mean of a random variable, where the goal is to produce the smallest possible interval for a given number of samples. While minimax optimal algorithms are known for this…

We study the problem of estimating the diagonal of an implicitly given matrix $A$. For such a matrix we have access to an oracle that allows us to evaluate the matrix vector product $Av$. For random variable $v$ drawn from an appropriate…

In this paper, two new classes of lower bounds on the probability of error for $m$-ary hypothesis testing are proposed. Computation of the minimum probability of error which is attained by the maximum a-posteriori probability (MAP)…

We propose and analyze a posteriori error estimators for an optimal control problem that involves an elliptic partial differential equation as state equation and a control variable that enters the state equation as a coefficient; pointwise…

A random variable $\xi$ has a {\it light-tailed} distribution (for short: is light-tailed) if it possesses a finite exponential moment, $\E \exp (\lambda \xi) <\infty$ for some $\lambda >0$, and has a {\it heavy-tailed} distribution (is…