Related papers: A Note on New Bernstein-type Inequalities for the …

We obtain a Bernstein-type inequality for sums of Banach-valued random variables satisfying a weak dependence assumption of general type and under certain smoothness assumptions of the underlying Banach norm. We use this inequality in order…

We establish a new Bernstein-type deviation inequality for general (non-reversible) discrete-time Markov chains via an elementary approach. More robust than existing works in the literature, our result only requires the Markov chain to…

We improve and subsume the conditions of Johansson and \"Oberg [18] and Berbee [2] for uniqueness of a g-measure, i.e., a stationary distribution for chains with complete connections. In addition, we prove that these unique g-measures have…

For a polynomial $P_n$ of degree $n$, Bernstein's inequality states that $\|P_n'\| \le n \|P_n\|$ for all $L^p$ norms on the unit circle, $0<p\le\infty,$ with equality for $P_n(z)= c z^n.$ We study this inequality for random polynomials,…

We derive explicit Bernstein-type and Bennett-type concentration inequalities for matrix-valued martingale processes with unbounded observations from the Hermitian space $\mathbb{H}(d)$. Specifically, we assume that the…

Known Bernstein-type upper bounds on the tail probabilities for sums of independent zero-mean sub-exponential random variables are improved in several ways at once. The new upper bounds have a certain optimality property.

It is well known that there is no direct one-to-one relation between $p$-values and likelihood ratios or Bayes factors, since their relation crucially involves the sample size $n$. We investigate their (asymptotic) relation in a…

Studying the effects of one-way variation of any number of parameters on any number of output probabilities quickly becomes infeasible in practice, especially if various evidence profiles are to be taken into consideration. To provide for…

Latent variable models are frequently used to identify structure in dichotomous network data, in part because they give rise to a Bernoulli product likelihood that is both well understood and consistent with the notion of exchangeable…

We prove concentration inequalities for functions of independent random variables {under} sub-gaussian and sub-exponential conditions. The utility of the inequalities is demonstrated by an extension of the now classical method of Rademacher…

We present Hoeffding-type and Bernstein-type inequalities for right-censored data. The inequalities bound the difference between an inverse of the probability of censoring weighting (IPCW) estimator and its expectation. We first discuss the…

In this work, a generalization of the well known Bernoulli inequality is obtained by using the theory of discrete fractional calculus. As far as we know our approach is novel.

In this paper, we provide a new and sharper bound for the Legendre coefficients of differentiable functions and then derive a new error bound of the truncated Legendre series in the uniform norm. The key idea of proof relies on integration…

We show that the log-likelihood of several probabilistic graphical models is Lipschitz continuous with respect to the lp-norm of the parameters. We discuss several implications of Lipschitz parametrization. We present an upper bound of the…

In this paper, we establish several new versions of Bohr-type inequalities for bounded analytic functions in the unit disk by allowing $\varphi=\{\varphi_n(r)\}^{\infty}_{n=0}$ in place of the $\{r^n\}^{\infty}_{n=0}$ in the power series…

We address the issue of performing inference on the parameters that index a bimodal extension of the Birnbaum-Saunders distribution (BS). We show that maximum likelihood point estimation can be problematic since the standard nonlinear…

We shed new light on Heisenberg's uncertainty principle in the sense of Beurling, by offering an essentially different proof which permits us to weaken the assumptions substantially, and examples show that the result is sharp. The proof…

A fundamental problem in network data analysis is to test Erd\"{o}s-R\'{e}nyi model $\mathcal{G}\left(n,\frac{a+b}{2n}\right)$ versus a bisection stochastic block model $\mathcal{G}\left(n,\frac{a}{n},\frac{b}{n}\right)$, where $a,b>0$ are…

In this note, we prove a tight lower bound on the joint entropy of $n$ unbiased Bernoulli random variables which are $n/2$-wise independent. For general $k$-wise independence, we give new lower bounds by adapting Navon and Samorodnitsky's…

We extend the classical Bernstein inequality to a general setting including Schr{\"o}dinger operators and divergence form elliptic operators on Riemannian manifolds or domains. Moreover , we prove a new reverse inequality that can be seen…