Abstract
For a sequence {x n , n ≥ 1} of φ-mixing random variables and a triangular array of constants {a n ,k,1≤k≤n,n≥ 1} conditions are given to ensure that (Formula presented.) where {b n } 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.
Original language | English |
---|---|
Pages (from-to) | 3882-3894 |
Journal | Communications in Statistics - Theory and Methods |
Volume | 49 |
Issue number | 16 |
DOIs | |
Publication status | Published - 17 Aug 2020 |
Keywords
- mixing
- strong consistency
- weighted sum