Almost sure convergence for weighted sums of φ-mixing random variables with applications

João Lita da Silva

Communications in Statistics - Theory and Methods, 2020, vol. 49, issue 16, 3882-3894

Abstract: For a sequence {Xn, n ⩾ 1} of φ-mixing random variables and a triangular array of constants {an,k,1⩽k⩽n,n ⩾ 1} conditions are given to ensure that ∑k=1nan,k(Xk−E Xk)/bn→a.s.0, where {bn} is a prescribed sequence of positive constants. Our statements are established at the extension of a Rosenthal type inequality for φ-mixing random variables and discard any assumption on the mixing coefficient. The proposed results are employed in well-known estimators arising from regression models in order to obtain its strong consistency.

Date: 2020
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DOI: 10.1080/03610926.2019.1594302

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