Course in Robust Statistical Methods
ECE 5714 - Robust Estimation and Filtering
SPRING 2008, M 4:00 pm
INSTRUCTOR: Dr. L. Mili, NVC 438, Tel: (703) 538 3767, E-mail: lmili@vt.edu
PREREQUISITES: This course requires a basic knowledge in probability and statistics as
covered in STAT 4714.
TEXTBOOKS: Class notes will be distributed throughout the semester.
REFERENCE BOOKS:
- David C. Hoaglin, Frederick Mosteller, John W. Tukey. Understanding Robust and
Exploratory Data Analysis. John Wiley, 1983.
- F. R. Hampel et al. Robust Statistics: The Approach Based on Influence Functions. John
Wiley 1986.
- R. G. Staudte and S. J. Sheather. Robust Estimation and Testing. John Wiley 1990.
- Peter J. Rousseeuw and Annick M. Leroy. Robust Regression and Outlier Detection. John
Wiley, 1987.
- R. A. Maronna, R. D. Martin, and V. J. Yohai. Robust Statistics-Theory and Methods. John
Wiley, 2006.
- A. Abur and A. G. Exposito. Power System State Estimation-Theory and Implementation.
Marcel Dekker, 2004.
- J. Astola and P. Kuosmanen. Fundamentals of Nonlinear Digital Filtering. CRC Press, 1997.
- J. Baran. Statistics for Long-Memory Processes. Chapman & Hall, 1994.
- K. Park and W. Willinger (Editors). Self-Similar Network Traffic and Performance
Evaluation. John Wiley, 2000.
OBJECTIVE: An introduction to optimal and robust estimation and filtering as applied to
engineering problems such as speech processing, image processing, Internet data processing,
detection in radar systems, system identification, measurement calibration, power system state
estimation and load forecasting, and electric price forecasting.
OFFICE HOURS:
Mondays: 7:00 – 8:00 PM, NVC 438
Wednesdays: 7:00 – 8:00 PM, NVC 438
Thursdays: 3:00 – 5:00 PM, NVC 438
GRADING
Homework 30%
Midterm Test 35%
Final Exam (Project) 35%
HOMEWORK: Assigned homework will be collected in class on due time. Late homework will
be penalized.
MIDTERM TEST: The test will be in class, and open book/notes.
FINAL EXAM: The final exam will be of the take-home type. It consists of a project work and a
report.
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HONOR SYSTEM: Honor system rules apply to all your work. It is your understanding
that should be reflected in all work that you turn in. See http://ghs.grads.vt.edu/:
“In working on projects and homework, discussion and cooperative learning on general
topics is encouraged. Such discussion must be limited to general information such as
lecture and text material. Using another student’s solution, design, implementation, or
other specific results is strictly prohibited and is an honor code violation. Copying
computer files or designs from any source is strictly prohibited and is an honor code
violation. The midterm and final exams must be the work of the student. Consulting any
other person except the instructor for this course about any aspect of an exam is strictly
prohibited and is an honor code violation. Ask the instructor if you ever have a question
about what is acceptable or unacceptable sharing.”
DISABILITY ACCOMODATION: Reasonable accommodations are available for students who
have documentation of a disability from a qualified professional. Students should contact the
Services for Students with Disabilities (SSD). Any student with accommodations through the
SSD Office should contact me during the first two weeks of the semester.
RELIGIOUS ACCOMODATION: If participation in some part of this class conflicts with your
observation of specific religious holidays during the semester, please contact me during the first
two weeks of class to make alternative arrangements.
ACCOMODATION FOR MEDICAL OR PERSONAL/FAMILY EMERGENCIES:
If you miss class due to illness, especially in the case of an exam or some deadline, contact a
professional in Schiffert Health Center. If deemed appropriate, documentation of your illness will
be sent to the Dean’s Office for distribution to me. If you experience a personal or family
emergency that necessitates missing class, contact the Dean of Students at (540) 231 3787.
______________________________________
COURSE OUTLINE
1 - Estimation of location and Scale
1.1 Estimators of location
1.2 Estimators of scale
1.3 Outlier identification methods
2 - Probability Distribution Theory
2.1 The Gaussian distribution
2.2 The Laplacian distribution
2.3 The Cauchy distribution
2.4 The Student distribution
2.5 Mixture of probability distributions
3 - Parametric Estimation Theory
3.1 Maximum Likelihood estimators
3.2 Fisherian concept of consistency and efficiency
3.3 Equivariance properties of an estimator
4 - M-estimators
4.1 Definition
4.2 Sub-classes of M-estimators
4.3 Properties of the M-estimators
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5 - Robustness concepts
5.1 Qualitative robustness
5.2 The breakdown point
5.3 The influence function
6 - Regression estimators
6.1 Simple regression
6.2 Least squares estimator
6.3 M-estimators
6.4 Robust estimation of multivariate location and covariance
6.5 Leverage point identification
6.6 Generalized M-estimators
7 - Robust filters
7.1 The auto-regressive model
7.2 Least squares estimation of AR models
7.3 Robust estimation of AR models
7.4 Robust estimation of ARMA models
8 – Long-Memory and Self-Similar Processes
8.1 Definitions
8.2 Hurst coefficient estimation
8.3 Estimation of fractional ARIMA models
9 - Kalman Filter
9.1 The model
9.2 Classical Kalman filter
9.3 Robust Kalman filter
10 - High-Breakdown estimators
10.1 Least Trimmed squares estimator
10.2 Least median of squares
10.3 The resampling method
11 - Applications
11.1 Image processing
11.2 Radar systems
11.3 Internet data processing
11.4 Power system state estimation and load forecasting
Published by Bill Frakes on February 15 of 2008
