Foundations and Applications of Mathematical Statistics: A Theoretical and Practical Perspective
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Abstract
Mathematical statistics serves as the backbone of modern data analysis, providing rigorous methodologies for inference, estimation, and hypothesis testing. This paper presents a comprehensive overview of the fundamental principles, key theorems, and applications of mathematical statistics, emphasizing its interplay with probability theory and computational techniques. We discuss parametric and non-parametric approaches, regression analysis, Bayesian inference, and emerging challenges in high-dimensional statistics. The paper concludes with insights into future research directions, particularly in machine learning and robust statistical methods.
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