·       Overview of the parameter estimation problem

·       Estimation in parametric families:

o   Minimum variance unbiased estimation

o   Fisher information and the Cramer-Rao lower bound

o   Linear models: Linear regression and best linear unbiased estimation

o Sufficient statistics: The Neyman-Fisher factorization Theorem; the Rao-Blackwell-Lehmann-Scheffe Theorem; exponential families

o   Maximum likelihood estimation and its asymptotic properties

o   Maximum spacing estimation

o   The least squares approach

·       Bayesian estimation:

o   MMSE estimation

o   Maximum A-Posteriori estimation and conjugate priors

o   Linear MMSE estimation, Wiener filtering

o   Kalman filtering

·       Algorithms:

o   Sequential estimation

o   Expectation—Maximization and Alternating—Minimization

·       Detection theory:

o   The Bayesian approach

o   The Neyman-Pearson Approach

o   Composite hypothesis testing

·       Advanced topics

o   Regularization techniques and sparse models

o   Robust estimation

o   Minimax estimators