Almost sure convergence for weighted sums of pairwise PQD random variables

We obtain Marcinkiewicz-Zygmund strong laws of large numbers for weighted sums of pairwise positively quadrant dependent random variables stochastically dominated by a random variable $X \in \mathscr{L}_{p}$, $1 \leqslant p < 2$. We use our results to establish the strong consistency of estimators which emerge from regression models having pairwise positively quadrant dependent errors.Comment: 20 page

On some linear recurrences

The solution for a type of linear homogeneous recurrence relation with constant coefficients is presented with the help of Chebyshev polynomials of the second kind. An application to ladder networks is provided.authorsversionpublishe

The characteristic polynomial of some anti-tridiagonal 2-Hankel matrices of even order

In this paper, we derive the characteristic polynomial for a family of anti-tridiagonal 2-Hankel matrices of even order in terms of Chebyshev polynomials, giving also a representation of its eigenvectors. An orthogonal diagonalization for these type of matrices having null northeast-to-southwest diagonal is also provided using prescribed eigenvalues.authorsversionpublishe

On the spectral properties of real antitridiagonal Hankel matrices

Funding Information: Funding information : This work is a contribution to the Project UIDB/04035/2020, funded by FCT - Fundação para a Ciência e a Tecnologia, Portugal. Publisher Copyright: © 2023 João Lita da Silva, published by De Gruyter.In this article, we express the eigenvalues of real antitridiagonal Hankel matrices as the zeros of given rational functions. We still derive eigenvectors for these structured matrices at the expense of prescribed eigenvalues.publishersversionpublishe

Some comments on Chen Xu, Mengmei XI, Xuejun wang and Hao Xia’s paper “LR convergence for weighted sums of extended negatively dependent random variables”

This work is a contribution to the Project UIDB/04035/2020, funded by FCT - Fundacao para a Ciencia e a Tecnologia, Portugal.In this short note, we show that an assertion presented in the main result of Chen Xu, Mengmei Xi, Xuejun Wang and Hao Xia’s paper, “Lr convergence for weighted sums of extended negatively dependent random variables”, is false. A reformulation of this statement is announced making it valid.publishersversionpublishe

On the convergence of series of moments for row sums of random variables

UIDB/04035/2020Given a triangular array 1 of random variables satisfying 1 and sequences {bn}, {cn} of positive real numbers, weshall prove that ∞ < 1, where x+ = max(x, 0). Our results are announced in a general setting, allowing us to obtain the convergence of the series in question under various types of dependence.publishersversionpublishe