Almost sure convergence for weighted sums of pairwise PQD random variables

João Lita da Silva

doi:10.1080/03610926.2022.2154129

Almost sure convergence for weighted sums of pairwise PQD random variables

João Lita da Silva

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Abstract

We obtain strong laws of large numbers of Marcinkiewicz–Zygmund’s type for weighted sums of pairwise positively quadrant dependent random variables stochastically dominated by a random variable (Formula presented.) We use our results to establish the strong consistency of estimators which emerge from regression models having pairwise positively quadrant-dependent errors.

Original language	English
Number of pages	24
Journal	Communications in Statistics - Theory and Methods
DOIs	https://doi.org/10.1080/03610926.2022.2154129
Publication status	Published - 21 Dec 2022

Keywords

positively quadrant dependent random variables
regression models
strong consistency
Strong law of large numbers
weighted sum

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10.1080/03610926.2022.2154129

WeightedPQDR3Accepted author manuscript, 245 KBLicence: CC BY-NC-ND

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AB - We obtain strong laws of large numbers of Marcinkiewicz–Zygmund’s type for weighted sums of pairwise positively quadrant dependent random variables stochastically dominated by a random variable (Formula presented.) We use our results to establish the strong consistency of estimators which emerge from regression models having pairwise positively quadrant-dependent errors.

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KW - weighted sum

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Almost sure convergence for weighted sums of pairwise PQD random variables

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