Tail probability bounds for acceptable random variables of partial sums and their application in linear models
Year: 2024
Type: article
Abstract: Exponential probability inequalities play an important role in many parts of probability and statistics, offering a fundamental tool for tail probability bounding and modeling stochastic processes. The present work proposes a new exponential inequality for acceptable random variables. This class covers dependencies that are not embraced by the standard independence assumptions. Our results extend the theoretical perspective by placing sharper bounds on the above-mentioned variables, which tends to increase the accuracy of probabilistic modeling. Moreover, we study complete convergence in first-order autoregressive processes with acceptable innovations. The complete convergence framework gives further insights into the long-term behavior of the wide class of processes commonly used in time series analysis, econometrics, and other areas of applied research. In turn, our results on the influence of acceptable innovations on the properties of complete convergence establish bridges between theoretical probability inequalities and statistical applications. In addition, these contributions provide new tools in investigating the stability and predictability of the autoregressive models. These considerations consequently set up significant perspectives and enrich a developing body of research related to stochastic processes by reinforcing the theoretical framework as well as the methodological apparatus of probability theory.
Authors: Ikhlasse Chebbab, Insaf Chebbab, Samir Benaissa, Chouaib Bourahla
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4404107312