Theory of Statistics 1 - KSU

1. Sampling Distribution and Central Limit Theorem. 2. Estimator Properties: Unbiasedness – Mean Squared Error – Consistency – Sufficiency – Minimal Sufficiency – Completeness - Minimum Variance Unbiased Estimator. 3. Exponential Family Theorem. 4. Fisher Information and Cramer-Rao Inequality. 5. Rao-Blackwell and Lehmann-Scheffé Theorems. 6. Estimation Methods: Method of Moments – Maximum Likelihood Method. 7. Bayesian Estimate: Prior and Posterior Distributions – Loss Function Approach