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General Bahr-Esseen inequalities and their applications
István Fazekas1, Sándor Pecsora1
1Faculty of Informatics, University of Debrecen, P.O. Box 400, Debrecen, 4002 Hungary.
Journal of Inequalities and Applications
|September 5, 2017
Summary
The Bahr-Esseen inequality holds with exponent p if it is true for truncated variables. This finding advances understanding of the inequality and its applications in probability theory.
Area of Science:
- Probability Theory
- Mathematical Statistics
Background:
- The Bahr-Esseen inequality is a fundamental result in probability theory.
- Understanding the conditions under which this inequality holds is crucial for developing robust statistical methods.
Purpose of the Study:
- To establish new conditions for the validity of the Bahr-Esseen inequality.
- To extend the applicability of the Bahr-Esseen inequality to a broader range of random variables.
- To demonstrate the practical implications of these findings for limit theorems.
Main Methods:
- Analysis of the Bahr-Esseen inequality for truncated and centered random variables.
- Investigation of the relationship between the inequality's validity for different exponents.
- Application of established theoretical frameworks to prove the main results.
Main Results:
- Demonstrated that the Bahr-Esseen inequality holds for exponent p if it holds for a specific related exponent with truncated and centered random variables.
- Proved the inequality's validity when truncated random variables are deemed acceptable.
- Established the direct applicability of these refined conditions to derive weak and strong laws of large numbers and complete convergence.
Conclusions:
- The study provides a more generalized understanding of the Bahr-Esseen inequality.
- The findings facilitate the derivation of important limit theorems under less restrictive conditions.
- This research contributes to the theoretical underpinnings of statistical inference and analysis of random phenomena.
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