Applying Asymptotic Normality of OLS Coefficients in Humanities: A Methodological Bridge between Random Simulation and Sampling Theory in Cultural and Historical Research

Abstract

In the ever-evolving landscape of humanities research, the integration of quantitative methods offers profound insights into cultural and historical studies. This paper explores the application of Ordinary Least Squares (OLS) model coefficients, particularly focusing on their asymptotic normality, within humanities sciences. We delve into the theoretical underpinnings of OLS estimates, utilizing random simulation and sampling theory to illustrate the robustness and reliability of these methods in non-traditional contexts. Through a series of simulations, we demonstrate how the asymptotic properties of OLS estimators can provide a nuanced understanding of complex humanities data, bridging the gap between quantitative rigor and qualitative richness. We argue that the application of such statistical models empowers humanities researchers to uncover patterns and relationships that might otherwise remain obscured in purely qualitative analyses. Furthermore, we discuss the implications of this methodological integration for future cultural and historical research, suggesting a paradigm shift towards a more interdisciplinary approach in understanding humanistic phenomena. This study not only reaffirms the relevance of statistical methods in the humanities but also provides a practical framework for their application, promising a richer, more nuanced understanding of the human experience.