| 1 | Estimation Theory
Introduction | |
| 2 | Some Probability Distributions | Problem set 1 out |
| 3 | Method of Moments | |
| 4 | Maximum Likelihood Estimators | Problem set 2 out |
| 5 | Consistency of MLE
Asymptotic Normality of MLE, Fisher Information | |
| 6 | Rao-Crámer Inequality | |
| 7 | Efficient Estimators | Problem set 3 out |
| 8 | Gamma Distribution
Beta Distribution | |
| 9 | Prior and Posterior Distributions | |
| 10 | Bayes Estimators
Conjugate Prior Distributions | Problem set 4 out |
| 11 | Sufficient Statistic | |
| 12 | Jointly Sufficient Statistics
Improving Estimators Using Sufficient Statistics, Rao-Blackwell Theorem | |
| 13 | Minimal Jointly Sufficient Statistics
χ2 Distribution | Problem set 5 out |
| 14 | Estimates of Parameters of Normal Distribution | |
| 15 | Orthogonal Transformation of Standard Normal Sample | |
| 16 | Fisher and Student Distributions | |
| 17 | Confidence Intervals for Parameters of Normal Distribution | |
| 18 | Testing Hypotheses
Testing Simple Hypotheses
Bayes Decision Rules | |
| 19 | Most Powerful Test for Two Simple Hypotheses | Problem set 6 out |
| 20 | Randomized Most Powerful Test
Composite Hypotheses, Uniformly Most Powerful Test | |
| 21 | Monotone Likelihood Ratio
One Sided Hypotheses | |
| 22 | One Sided Hypotheses (cont.) | Problem set 7 out |
| 23 | Pearson's Theorem | |
| 24 | Goodness-of-Fit Test
Goodness-of-Fit Test for Continuous Distribution | |
| 25 | Goodness-of-Fit Test for Composite Hypotheses | |
| 26 | Test of Independence | |
| 27 | Test of Homogeneity | Problem set 8 out |
| 28 | Kolmogorov-Smirnov Test | |
| 29 | Simple Linear Regression
Method of Least Squares
Simple Linear Regression | |
| 30 | Joint Distribution of the Estimates | |
| 31 | Statistical Inference in Simple Linear Regression | Problem set 9 out |
| 32 | Classification Problem | |