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We propose a new finite sample corrected variance estimator for the linear generalized method of moments (GMM) including the one-step, two-step, and iterated estimators. Our formula additionally corrects for the over-identification bias in…
We present a general analysis of the bifurcation sequences of 2:2 resonant reversible Hamiltonian systems invariant under spatial $\Z_2\times\Z_2$ symmetry. The rich structure of these systems is investigated by a singularity theory…
We deduce the non-asymptotical bilateral estimates for moment inequalities for sums of non-negative independent random variables, based on the correspondent estimates for the so-called Bell functions and the Poisson distribution.
There are numerous examples of natural and artificial processes that represent stochastic sequences of events followed by an absolute refractory period during which the occurrence of a subsequent event is impossible. In the simplest case of…
We use classical results from harmonic analysis on matrix spaces to investigate the relation between the joint density of the singular values and of the eigenvalues of complex random matrices which are bi-unitarily invariant (also known as…
The problem of convergence of moments of a sequence of random variables to the moments of its asymptotic distribution is important in many applications. These include the determination of the optimal training sample size in the cross…
We derive two-sided bounds for moments and tails of random quadratic forms (random chaoses of order $2$), generated by independent symmetric random variables such that $\lVert X \rVert_{2p} \leq \alpha \lVert X \rVert_p$ for any $p\geq 1$…
This work obtains sharp closed-form exponential concentration inequalities of Bernstein type for the ubiquitous beta distribution, improving upon sub-gaussian and sub-gamma bounds previously studied in this context. The proof leverages a…
We give a comparison inequality that allows one to estimate the tail probabilities of sums of independent Banach space valued random variables in terms of those of independent identically distributed random variables. More precisely, let…
We establish inverse and direct theorems on best approximations in quasi-normed Abelian groups through bilateral Bernstein-Jackson inequalities with exact constants. Using integral representations for quasi-norms of functions $f$ in…
In this paper we consider the numerical approximation of a general second order semi-linear parabolic partial differential equation. Equations of this type arise in many contexts, such as transport in porous media. Using finite element…
We derive sharp non - asymptotical Lebesgue - Riesz as well as Grand Lebesgue Space norm estimations for different norms of matrix martingales through these norms for the correspondent martingale differences and through the entropic…
We consider uniform moment convergence of lag-window spectral density estimates for univariate and multivariate stationary processes. Optimal rates of convergence are obtained under mild and easily verifiable conditions. Our theory…
An exact upper bound on the Winsorised-tilted mean of a symmetric random variable in terms of its second moment is given. Such results are used in work on nonuniform Berry--Esseen-type bounds for general nonlinear statistics.
Linear stationary reaction-convection-diffusion equations with Dirichlet boundary conditions are approximated using a simple finite difference method corresponding to central differences and the addition of a high-order stabilization term…
We consider Khintchine type inequalities on the $p$-th moments of vectors of $N$ $k$-wise independent Rademacher random variables. We show that an analogue of Khintchine's inequality holds, with a constant $N^{1/2-k/2p}$, when $k$ is even.…
We investigate the complete $p$-th moment convergence for weighted sums of independent, identically distributed random variables under sublinear expectations space. Using moment inequality and truncation methods, we prove the equivalent…
This paper deals with the comparison of several stationary processes with unequal sample sizes. We provide a detailed theoretical framework on the testing problem for equality of spectral densities in the bivariate case, after which the…
We analyze the assumptions that are made in the proofs of Bell-type inequalities for the results of Einstein-Podolsky-Rosen type of experiments. We find that the introduction of time-like random variables permits the construction of a…
In this paper we obtain a Bernstein type inequality for the sum of self-adjoint centered and geometrically absolutely regular random matrices with bounded largest eigenvalue. This inequality can be viewed as an extension to the matrix…