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