Part VII — Asymptotic Theory

What happens as the sample grows. The three modes of convergence — almost surely, in probability, and in distribution — organize this part: the weak and strong laws of large numbers, the Central Limit Theorem, and the mapping theorems (delta method, Slutsky, continuous mapping) that turn them into usable asymptotics.

Topics

Topic	Focus
The Weak Law of Large Numbers	Markov and Chebyshev inequalities and convergence of sample means in probability
The Strong Law of Large Numbers	Almost-sure convergence of sample means
The Central Limit Theorem	Convergence in distribution of standardized sums to the normal
The Delta Method	Asymptotic distributions of smooth functions of estimators
Slutsky's Theorem	Combining convergence in distribution with convergence in probability
Continuous Mapping Theorem	Convergence preserved under continuous transformations