Core content

  1. Probability Review (2 weeks)
    1. Random Variables
    2. Concentration inequality (non-asymptotic theory)
    3. Limit Theorems (asymptotic theory)
    4. Special distributions
  2. Sampling distribution, confidence interval (Rice, 6.3, 7.1 – 7.3) (1 week)
  3. Parameter estimation & Method of moments (Rice, 8.1 – 8.4) (1 week)
  4. Maximum likelihood estimation (Rice, 8.5) (1 week)
  5. Expection-Maximization Algorithm (Wasserman, 9.13.4) (1 week)
  6. Bayesian approach to parameter estimation (Wasserman, 11) (1 week)
  7. Unbiased estimators, Efficiency & Cramer-Rao Inequality (Casella & Berger, 7.3.2, Rice, 8.7) (1 week)
  8. Sufficiency and unbiasedness, Rao-Blackwell Theorem (Casella & Berger, 7.3.3, Rice, 8.8) (1 week)
  9. Hypothesis testings, Neyman-Pearson Lemma, Wald test, Likelihood Ratio test (Rice, 9) (2 weeks)
  10. Comparing samples (Rice, 11) (1 week)
  11. Analysis of Variance (Rice, 12) (1 week)
  12. Linear regression and least squares (Wasserman, 13.1-13.3, Casella & Berger, 11.3) (1 week)