Strong Convergence for Weighted Sums of Widely Orthant Dependent Random Variables and Applications

Wu, Yi; Wang, Xuejun; Shen, Aiting

doi:10.1007/s11009-023-09976-3

Methodol Comput Appl Probab

2023

DOI: 10.1007/s11009-023-09976-3

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Strong Convergence for Weighted Sums of Widely Orthant Dependent Random Variables and Applications

Yi Wu

Xuejun Wang

Aiting Shen

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2024

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Cited by 2 publications

References 41 publications

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Strong convergence for weighted sums of (α, β)-mixing random variables and application to simple linear EV regression model

Hu,

Wang,

2024

Open Mathematics

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In this article, the complete convergence and the Kolmogorov strong law of large numbers for weighted sums of ( α , β ) \left(\alpha ,\beta ) -mixing random variables are presented. An application to simple linear errors-in-variables model is provided. Simulation studies are also carried out to support the theoretical results.

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Strong convergence for weighted sums of (α, β)-mixing random variables and application to simple linear EV regression model

Hu,

Wang,

2024

Open Mathematics

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Strong limit theorems for weighted partial sums of widely orthant dependent series and probability inequalities with applications to first order autoregressive models

Cherifi,

Benaissa,

Mechab

et al. 2024

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This study investigates widely orthant dependent random variables, establishing probability inequalities and deriving their key properties, which are essential for the development of strong limit theorems. These random variables define a specific structure of dependence that plays a crucial role in understanding various statistical challenges in both theoretical and applied contexts. Building on these foundational results, we extend the Khinchin-Kolmogorov convergence theorem and the three series convergence theorem to the case of widely orthant dependent random variables. Additionally, we derive strong limit theorems for weighted sums of widely orthant dependent random variables, extending existing findings in the literature . The core theoretical contributions are demonstrated through their application to first order autoregressive models, emphasizing the relevance of these results in time series analysis. Numerical simulations are conducted to verify and visualize the theoretical findings, showcasing their applicability and robustness. These results provide insights into the behavior of widely orthant dependent random variables and contribute to the advancement of statistical theory.

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Strong Convergence for Weighted Sums of Widely Orthant Dependent Random Variables and Applications

Cited by 2 publications

References 41 publications

Strong convergence for weighted sums of (α, β)-mixing random variables and application to simple linear EV regression model

Strong convergence for weighted sums of (α, β)-mixing random variables and application to simple linear EV regression model

Strong limit theorems for weighted partial sums of widely orthant dependent series and probability inequalities with applications to first order autoregressive models

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