Statistical Inference II

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" summary

Defines hypothesis testing with controlled Type I error α and power as rejection probability, explains uniformly most powerful tests and the chi-square vs. max-norm tradeoff for high-dimensional sparse signals (root(2 log D) vs. root(D)), shows confidence sets as duals of tests, and derives the asymptotic distribution of the maximum likelihood estimator: sqrt(n)(θ̂−θ0) → Normal(0, I(θ0)^{-1}) where Fisher information I(θ) = Var(∂ log p/∂θ).

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" chapters (13)

1. 0:00Introduction to hypothesis
2. 2:00Errors and significance levels
3. 4:49Power of a test
4. 7:31Uniformly most powerful test
5. 11:05Multiple sampling and minimax
6. 14:22Testing in high dimensions
7. 18:45Confidence intervals basics
8. 22:26Duality of tests and intervals
9. 25:48Confidence interval optimality
10. 30:59Duality examples and benefits
11. 36:52Interpretation of intervals
12. 40:25Maximum likelihood estimation
13. 54:04Asymptotic distribution