Asymptotic Thinking

Convergence, laws of large numbers, central limit theory, and approximation.

This level will connect probability foundations to large-sample statistical inference through convergence, the law of large numbers, the central limit theorem, and related approximations.

• Convergence in probability and almost-sure convergence

• Law of large numbers

• Convergence in distribution

• Central limit theorem

• Delta method

• Slutsky’s theorem and continuous mapping

• Asymptotic bias, consistency, and efficiency

• When asymptotic approximations fail

• Probability & Randomness

• Statistical Inference

• Statistics overview