An introduction to the analysis and design of maximum likelihood and robust estimators and filters. Maximum likelihood estimation theory: consistency, asymptotic efficiency, sufficiency. Robust estimation theory: qualitative robustness, breakdown point, influence function, change-of-variance function. Robust estimators: M-estimators, generalized M-estimators, high-breaddown estimators.
Why take this course?
Robust estimation theories have undergone important developments that need to be introduced in various engineering fields such as signal processing, communications, radar systems and electric power systems, to cite a few. The cornerstones of these developments are the robustness concepts of breakdown point and influence function that enable the student to perform the analysis and design of estimators with desired requirements in view of their applications to engineering problems.
Prerequisites: ECE 5605
This course requires a working knowledge of probability and stochastic processes as taught in 5605.
Major Measurable Learning Objectives
Explain maximum likelihood and robust estimation theories and methods;
Evaluate the asymptotic efficiency, the breakdown point and the influence function of an M-estimator;
Develop maximum likelihood and robust parameter estimation methods in regression and for ARMA models;
Develop robust Kalman filters and evaluate their statistical properties;
Estimate the parameters of Fractional ARIMA models for long memory processes;
Apply maximum likelihood and robust estimation methods to engineering systems.
Percentage of Course
Probability distribution theory
Robust estimators of location and scale
Maximum Likelihood estimation theory and methods
Robust estimation theories and methods
Robust estimators in regression and applications
Robust estimation of ARMA models and applications
Robust Kalman filter and applications
Estimation of Fractional ARIMA models and applications