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The Application of the Law of Large Number in Econometric
Subject area: Science,Engineering and Technology · Area of research: Science
Abstract
This paper explores the fundamental role of the Law of Large Numbers (LLN) in econometrics. The LLN, a cornerstone of probability and statistics, underpins many econometric techniques by ensuring that sample means converge to their expected values as the sample size increases, thus providing a foundation for reliable statistical inference. This article elucidates the importance of the LLN in guaranteeing stable long-term results for averages of random economic events, highlighting its crucial implications for estimation and hypothesis testing in econometric models (multiple regression model). Furthermore, the paper discusses the application of the LLN in where it justifies practices such as portfolio diversification, risk estimation, and asset pricing by enhancing the reliability of empirical estimates with larger datasets. Ultimately, this analysis underscores the LLN's significance in reinforcing the credibility of statistical inference in econometrics and financial econometrics, ensuring that empirical results become more accurate and robust with increasing data.
References
[1] Casella, George, and Berger, Roger L. (various editions). Statistical Inference.
[2] Davidson, James. (1994). Stochastic Limit Theory: An Introduction for Econometricians. Oxford University Press.
[3] Erdem İŞBİLEN 2023 The law of large numbers helps us make predictions about the long-term behavior of a random variable based on a large number of experiments.
[4] H. Stock and Mark W. Watson Probability and Measure Theory" Introduction to Econometrics" by James: The 4th Edition was published in 2018.
[5] Hogg, Robert V., McKean, Joseph W., and Craig, Allen T. (various editions). Introduction to Mathematical Statistics.
[6] Robert B. Ash and Catherine A. Doleans-Dade (2nd Edition, 2020):
[7] Ross, Sheldon M. (various editions). A First Course in Probability.
How to cite this paper
@article{1708489,
author = {Peter Nyam, A. Bishir, Kadiri Simon Angulu, Abba Muhammad Yalwa, Obalisa Yemisi Funmilola},
title = {The Application of the Law of Large Number in Econometric},
journal = {Iconic Research And Engineering Journals},
year = {2025},
volume = {8},
number = {11},
pages = {1018-1023},
issn = {2456-8880},
url = {https://www.irejournals.com/formatedpaper/1708489.pdf},
abstract = {This paper explores the fundamental role of the Law of Large Numbers (LLN) in econometrics. The LLN, a cornerstone of probability and statistics, underpins many econometric techniques by ensuring that sample means converge to their expected values as the sample size increases, thus providing a foundation for reliable statistical inference. This article elucidates the importance of the LLN in guaranteeing stable long-term results for averages of random economic events, highlighting its crucial implications for estimation and hypothesis testing in econometric models (multiple regression model). Furthermore, the paper discusses the application of the LLN in where it justifies practices such as portfolio diversification, risk estimation, and asset pricing by enhancing the reliability of empirical estimates with larger datasets. Ultimately, this analysis underscores the LLN's significance in reinforcing the credibility of statistical inference in econometrics and financial econometrics, ensuring that empirical results become more accurate and robust with increasing data.},
month = {May},
}