Empirical Process Theory

[pharringtonp19]

References

• Note Reference
• Lecture Reference

Key Topics

• [ ] Stochastic Process
• [ ] Cartheadory Theorem
• [ ] regular: complete separable metric space
• [ ] Regular Conditional Probability
• [ ] Fubini's Theorem
  • [ ] Transition Kernel
• [ ] SLLN
• [ ] Glivenko-Cantelli
• [ ] Donsker theorems
  • [ ] standard Brownian bridge process

Papers

• [ ] A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics

[pharringtonp19]

How should I think about the following:

$$\underset{f \in \mathcal{F}}{\sup} \Big| \frac{1}{n} \sum f(X_i) - \mathbb{E}[f(X_i)]\Big|$$