Theory of Estimation

1. Point estimation: method of moments, maximum likelihood and least squares methods.
2. Properties of Estimators: Unbiased estimators. Sufficiency: joint, minimal, and complete statistics. Minimum variance unbiased estimators. Consistent and efficient estimators.
3. Cramer-Rao inequality for a single parameter.
4. Interval estimation. Mean squared error. Loss and risk functions.
5. Bayes' estimation. Mini max estimation.