Statistics 200C

Theoretical Statistics

Spring Quarter, 2010

Time & Place: MWF at 1:00, 5203 Math Sci.
Th at 1:00, 6201 Math Sci.

Instructor: Thomas S. Ferguson

Generalized Office Hour: Thurs. 1:00 pm. in 6201 Math. Sci.

Other Office Hours: Door usually open after 3:00 pm. 8917 Math. Sci. and by appointment.
E-mail: tom@math.ucla.edu

Generalized Reader: Jaishen Yu, office hour: 3:30-4:30 Wed.

Prerequisites: Statistics 200B or consent of instructor.
Topics: Large sample properties of tests and estimates, consistency and efficiency, U-statistics, chi-squared tests.
There will be one midterm in the sixth week. The final examination is on Thursday, June 10, from 11:30 AM to 2:30 PM.

Homework problems from Additional Exercises.: (due on Fridays)

  • Exercise Set 1. Problems 1.4 and 2.1 a,b,c. Solutions.
  • Exercise Set 2. Problems 2.7, 3.5 and 4.1. Solutions.
  • Exercise Set 3. Problems 5.5, 5.6 and 6.3. Solutions.
  • Exercise Set 4. Problems 7.8, 8.2 and 9.6. Solutions.
  • Exercise Set 5. Problems 10.3, 11.3 and 12.2. Solutions.
  • Exercise Set 6. Problems 12.4 and 13.2. Solutions.
  • Midterm Examination and Solutions.
  • Exercise Set 7. Problem 14.1. Solutions.
  • Exercise Set 8. Problems 17.4, 18.6 and 19.3. Solutions.
  • Exercise Set 9. Problems 20.5, 22.1 and 22.5. Solutions.
  • Exercise Set 10. Problems 24.1, 24.4 and 24.6. Solutions.
  • Last Year's Final Examination and Solutions.
  • This Year's Final Examination and Solutions.
  • Stein's Normal Approximation Theorem.
  • U-Statistics.
  • Distribution Function Calculators.

    Text: A Course in Large Sample Theory

    Chapman & Hall, 1996.
    Table of Contents

    Part 1: Basic Probability Theory.

    1. Modes of Convergence.
    2. Partial Converses.
    3. Convergence in Law.
    4. Laws of Large Numbers.
    5. Central Limit Theorems.

    Part 2: Basic Statistical Large Sample Theory

    6. Slutsky Theorems.
    7. Functions of the Sample Moments.
    8. The Sample Correlation Coefficient.
    9. Pearson's Chi-Square.
    10. Asymptotic Power of the Pearson Chi-Square Test.

    Part 3: Special Topics.

    11. Stationary m-dependent Sequences.
    12. Some Rank Statistics.
    13. Asymptotic Distribution of Sample Quantiles.
    14. Asymptotic Theory of Extreme Order Statistics.
    15. Asymptotic Joint Distributions of Extrema.

    Part 4: Efficient Estimation and Testing.

    16. A Uniform Strong Law of Large Numbers.
    17. Strong Consistency of the Maximum Likelihood Estimates.
    18. Asymptotic Normality of the MLE.
    19. The Cramer-Rao Lower Bound.
    20. Asymptotic Efficiency.
    21. Asymptotic Normality of Posterior Distributions.
    22. Asymptotic Distribution of the Likelihood Ratio Test Statistic.
    23. Minimum Chi-Square Estimates.
    24. General Chi-Square Tests.