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Advanced statistics course
·
Module 1
Convergence Concepts and Limit Theorems
1
Understanding Modes of Convergence
Define and distinguish between convergence in probability, convergence in distribution, and almost sure convergence
2
The Weak Law of Large Numbers
State and apply the Weak Law of Large Numbers
3
The Strong Law of Large Numbers
State and apply the Strong Law of Large Numbers
4
The Central Limit Theorem for i.i.d. Random Variables
State and apply the Central Limit Theorem for i.i.d. random variables
5
Asymptotic Distributions of Transformed Estimators: The Delta Method
Apply the delta method to derive asymptotic distributions of transformed estimators
6
Slutsky's Theorem: Combining Convergences
Use Slutsky's theorem to combine convergence results
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