Linear Statistical Inference

Fall Semester 2012

Last update: 11/28/2012
• Course Announcement

Time: Monday, Wednesday, Friday at 11:00 - 11:50 a.m.

Instructor: Jie Yang, SEO 513
Office Hours: Monday, Wednesday, Friday at 12:00 - 13:00 p.m.

Textbook: C. R. Rao,   Linear Statistical Inference and its Applications, 2nd edition, Wiley, 1973 (Reprinted in 2001).
Content: Estimation and testing in linear models, generalized inverses of matrices, n-dimensional normal distribution, quadratic forms, likelihood ratio tests, best invariant tests, analysis of variance
Prerequisite: STAT 411

Homework: Turn in every Friday before class;   half of the grade counts for completeness;  half of the grade counts for correctness of one selected problem
Midterms: October 3rd and November 14th, Wednesday, 11:00 a.m. - 11:50 a.m.
Final Exam: 10:30-12:30 p.m. Thursday, December 13
Grading: Homework 10%, midterms 25% each, final exam 40%
Grading Scale: 90% A , 80% B , 65% C , 50% D

Format of All Exams: Each exam is based on the homework and the examples discussed in class. The last class session before each exam is a review session. Please prepare any questions that you may have.

No makeup exam will be given without a valid excuse.

• Course Syllabus

 WEEK SECTIONS BRIEF DESCRIPTION 08/27 - 08/31 1a; 1b; 1b Vector Spaces; Theory of Matrices and Determinants 09/03 - 09/07 Holiday; 1c; 1c Eigenvalues and Reduction of Matrices 09/10 - 09/14 1d; 1e; 1f Convex Sets in Vector Spaces; Inequalities; Extrema of Quadratic Forms 09/17 - 09/21 3b; 8a; 8b Sampling Distributions; Multivariate Normal Distribution; Wishart Distribution 09/24 - 09/28 4a; 4a; 4a Theory of Least Squares (Linear Estimation) 10/01 - 10/05 Review; Midterm-1; 4b Tests of Hypotheses and Interval Estimation 10/08 - 10/12 4b; 4c, 4d; 4e Tests of Hypotheses and Interval Estimation; Problem of a Single Sample, One-Way Classified Data; Two-Way Classified Data 10/15 - 10/19 4e; 4f; 4g Two-Way Classified Data; General Model for Two-Way Data and Variance Components; Theory and Application of Statistical Regression 10/22 - 10/26 4g; 4g; 4h Theory and Application of Statistical Regression; General Problem of Least Squares with Two Sets of Parameters 10/29 - 11/02 4i; 4j; 4k Unified Theory of Linear Estimation; Estimation of Variance Components; Biased Estimation in Linear Models 11/05 - 11/09 5a; 5a; 5d Minimum Variance Unbiased Estimation; Some Methods of Estimation in Large Samples 11/12 - 11/16 Review; Midterm-2; 7a Testing of Statistical Hypotheses 11/19 - 11/23 7a; 7a; Holiday Testing of Statistical Hypotheses 11/26 - 11/30 7b; 7c; 7c Confidence Intervals; Sequential Analysis 12/03 - 12/07 7c; Review; Review Sequential Analysis 12/10 - 12/14 Final Exam Final Exam

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