Mathematical Statistics

数理统计 — An Interactive Journey

A rigorous, visualization-driven course through mathematical statistics, from probability foundations to asymptotic theory and modern resampling methods. Based on Casella & Berger, 陈希孺, and Hogg, McKean & Craig.

Course Roadmap

Part A: Probability Review 概率论回顾

  • Ch 0: Probability Spaces & Random Variables
  • Ch 1: Common Distribution Families
  • Ch 2: Multivariate Random Variables
  • Ch 3: Law of Large Numbers & Central Limit Theorem

Part B: Foundations of Statistical Inference 统计推断基础

  • Ch 4: Random Samples & Statistics
  • Ch 5: Sufficient Statistics & Completeness
  • Ch 6: Point Estimation
  • Ch 7: Evaluation Criteria

Part C: Interval Estimation & Hypothesis Testing 区间估计与假设检验

  • Ch 8: Confidence Intervals
  • Ch 9: Hypothesis Testing Fundamentals
  • Ch 10: Likelihood Ratio Tests
  • Ch 11: Common Tests

Part D: Regression & Advanced Topics 回归与高级主题

  • Ch 12: Linear Regression
  • Ch 13: Multiple Regression & Model Selection
  • Ch 14: Nonparametric Methods
  • Ch 15: Introduction to Bayesian Statistics

Part E: Asymptotic Theory & Modern Methods 渐近理论与现代方法

  • Ch 16: Asymptotic Theory
  • Ch 17: Bootstrap & Resampling Methods

Select a chapter from the sidebar to begin.