STAT 528   Mathematical Statistics   for Fall 2009

• Instructor: Jun Xie
  • Email: junxie@stat.purdue.edu
  • Mailbox in HAAS 164 (All homeworks are due on Thursday by 5:00pm).
  
  
• Course Schedule   TTH 3:00pm - 4:15pm, REC 123.
  
  • Midterm on Thur October 15, 2009, 8:00pm - 10:00pm, MSEE B012
    Midterm covers course materials up to Ch1.6.2.
  • Past Midterm Exam with Solutions
    Preparing for the final exam
    
  • Past Final Exam
  
  
• Office Hours:   Wed. 2:30-3:30pm and Thu. 1:00-2:00pm, HAAS 102.
  
  
• Prerequisite: STAT 519 is a prerequisite.
  The course is supposed to be taken by Ph.D. students of the department.
  Ph.D. students from outside of the department may also take it if they have the right backgrounds.
  
  
• Text Books: Mathematical Statistics: Basic Ideas and Selected Topics, Vol. 1, 2nd Edition,
  by Bickel and Doksum, Prentice Hall 2001.
  
  
• Syllabus: No probability will be taught.
  1. Review of probability theory.
     Apprendix A.1, A.8, B.2, A.13 in the text.
  2. Statistical models:
     • Data, models, statistics, parameters;
     • Decision theory (Bayes and minimax criteria, risk functions);
     • Bayesian models, conjugate prior distributions;
     • Prediction;
     • Sufficiency;
     • Exponential families.
     Ch 1 in the text.
  3. Estimation methods:
     • Method of Moments,
     • Least squares,
     • MLE,
     • EM algorithm.
     Ch2.1-2.3, 2.4.4.
  4. UMVU and information inequality.
     Ch3.4.
  5. Testing:
     • Neyman-Pearson Lemma,
     • UMP tests and monotone likelihood ratio models,
     • Likelihood ratio procedures.
     Ch4.1-4.3, Ch4.9.
  6. Asymptotic approximations:
     • Consistency,
     • Delta method,
     • Asymptotic normality of the MLE.
     Ch5.1-5.3.
  
  
• Grades: The grade is the cumulation of homework (20%), one midterm (30%), and the final exam (50%).
  
  
• Homework assignment
  All homeworks are due on Thursday by 5:00pm.
  No late homework will be accepted.
  The lowest homework will be dropped.