📊 Asymptotic Statistics

"Asymptotics is the art of replacing the impossible exact finite-sample distributions with the beautiful infinite-sample limits."

📈 Course Metadata

• Offered by: School of Mathematical Sciences & Center for Data Science

• Prerequisites: Mathematical Analysis, Advanced Algebra, Probability Theory, Mathematical Statistics, Functions of Real Variables, Functional Analysis (Recommended)

• Course Type: 32-hour PhD Core Course

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📚 References

The reference textbooks used in this course are as follows:

1. Course PPT: Special thanks to the instructor for providing detailed lecture slides. The logical structure and derivation paths of these MkDocs notes deeply reference the PPT's organization.

2. A.W. van der Vaart, Asymptotic Statistics (Cambridge University Press)

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🗺️ Syllabus & Navigation

Below is the directory for this course:

Part I: Foundations of Stochastic Convergence and Limit Theorems

• Chapter 1: Data Distributions and Stochastic Convergence

• Chapter 2: Characteristic Functions

• Chapter 3: Central Limit Theorem (Part I)

• Chapter 4: Central Limit Theorem (Part II)

Part II: Weakly Dependent Data

• Chapter 5: Weakly Dependent Data I

• Chapter 6: Weakly Dependent Data II

Part III: Asymptotic Inference Tools

• Chapter 7: Delta Method

• Chapter 8: Moment Estimator

• Chapter 9: MLE I

• Chapter 10: MLE II

• Chapter 11: M and Z Estimators I

• Chapter 12: M and Z Estimators II

• Chapter 13: U Statistics

• Chapter 14: Bootstrap

Part IV: 📝 Selected Solutions

• Homework 1 Solutions

• Homework 2 Solutions

• Homework 3 solutions

• Homework 4 solutions

📝 Notes & Formatting Details

Construction Complete

This page is now substantially complete. Long theorems and exercise solutions in the notes feature a folded box design. If you spot any typos, please feel free to raise an Issue or contact me directly for corrections!

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