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Mathematical Statistics

The difference between statistics majors and non-majors truly lies in Mathematical Statistics

It’s undeniable that statistics play a crucial role in modern human society, with applications in every scientific field. Whether it’s hypothesis testing or analytical techniques, a thorough understanding of statistics is essential for mastery in any domain. While the door to statistics is wide open even for non-majors, and many experts use statistical methods fluently within their specific domains—sometimes even more adeptly than majors—the fundamental difference lies in the level of mathematical understanding.

Majoring in statistics doesn’t just involve skimming through a few proofs and understanding the mathematical background of certain techniques. It’s about empathizing with the overarching concepts that run through statistics, having a clear understanding of the relationships between well-known distributions, and quickly grasping the principles behind new methods. Mathematical Statistics serves as both the study and training for this, encompassing the mathematical theories that underpin the entire field of statistics.

Probability Theory

For discussions involving measure theory at the level of Probability Theory, refer to the Measure Theory category.

Univariate Random Variables

Multivariate Random Vectors

Moments

Probability Distribution Theory

The study of Probability Distribution Theory in mathematical statistics is crucial but expansive. In this blog, due to its vast scope and inclusion of topics beyond mathematical statistics, it has been made a separate category.

Statistical Inference

Statistics

Unbiased Estimation

Sufficient Statistics

Likelihood Estimation

Hypothesis Testing

Interval Estimation

Bayesian

References

  • Casella. (2001). Statistical Inference(2nd Edition)
  • Hogg et al. (2013). Introduction to Mathematical Statistics(7th Edition)
  • 김달호. (2013). R과 WinBUGS를 이용한 베이지안 통계학

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