Fall 2001 Math 334 / Stat 434 at Lehigh University

This is the home page for Fall 2001 Math 334/Stat 434 ( Introduction to Mathematical Statistics ) at Lehigh University.
Math 334/Stat 434 (Mathematical Statistics): Popolations and random sampling; sampling distributions; theory of
estimation; criteria and methods of point and interval estimation; theory of testing statistical hypotheses.
Prerequiste: Math 231 or Math 309.
This course can be taken as a 400-level (3 graduate credits).

The text is "Statistics:Theory & Methods", 2nd edition, by Berry and Lindgren.

More information will follow later (or call me at (610) 758-3735).

Instructor: Professor Wei-Min Huang, Department of Mathematics. To contact me, send e-mail to wh02@Lehigh.EDU, or click here Mail-Me, if your web server supports forms. Click for Lehigh's home page or for Lehigh Mathematics Department home page.

Course syllabus (a pdf file)

Class Meeting:  M-W-F  10:10 - 11:00  AM,  XS203
    Homework:  Homework will be assigned almost every lecture.
                         It will be collected and graded by the instructor.
                         No late homework will be accepted.
              Tests: There will be two in-class tests and a Final Exam.

           Grades: Your course grade will be determined on the following basis.
                                Homework             25%
                                Projects & Tests     40%
                                Final Exam              35%

     References: Some other standard and advanced textbooks in mathematical statistics

          1.   Mathematical Statistics  by  P. J. Bickel  and  K. A. Doksum
          2.   Statistical Inference  by G. Casella and R. L. Berger
          3.   Theory of Point Estimation  by  E. L. Lehmann
          4.   Testing Statistical Hypotheses  by  E. L. Lehmann
          5.   Statistical Theory  by B. W. Lindgren
          6.   Linear Statistical Inference and Its Applications  by  C. R. Rao
          7.   Introduction to Mathematical Statistics by Hogg & Craig

For now I plan to cover the following topics:

  • Review (sample space, probability measure, conditional probability, independence, randon variables, some known discrete and continuous distributions, joint distributions, expected values, variance, covariance).
  • Understanding some important probability models
  • Relationships among common distributions
  • Transformation of random variables
  • Moments and Moment generating function
  • Can moments always uniquely determine a probability distributions?
  • Markov's inequality and Chebyshev's inequality
  • The moment-generating technique
  • Bivariate and multivariate normal distributions
  • Conditional probability and conditional expectation
  • Statistical independence
  • Approximate methods (delta-method and the continuous mapping theorem).
  • Limit theorems (Convergence in probability, LLN, Central Limit Theorem, and convergence in distribution).
  • Distribution derived from normal distribution (Chi-squared, t, F, and other related distributions).
  • Fitting the distribution (minimum chi-squared and other methods).
  • Unbiased and consistent estimator.
  • Method of moments, consistency of moment estimator.
  • Fisher Information and Cramer-Rao Inequality.
  • Exact vs Asymptotic variance, delta-method revisit.
  • Exact vs asymptotic distributions revisit.
  • Method of maximum Likelihood, large sample thoery for MLE.
  • Empirical Fisher information and approximate confidence interval based on MLE.
  • Regular (smooth) probability family.
  • Sufficient statistics and factorization theorem.
  • Sufficiency and Rao-Blackwell Theorem.
  • MVUE (Minimum Variance Unbiased Estimator).
  • Complete statistics and Lehmann-Scheffe Theorem.
  • Exponential probability family.
  • Order statistics.
  • Hypotheses testing.
  • Probabilities of Type-I and Type-II errors; Power function.
  • N-P Lemma.
  • Likelihood ratio tests.
  • Some resampling methods

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    For now the Homework Assignments are:

    1. HW #1: Problems 1.4,6(d,e,h),11,12,13 (chapter 1, pages 13,17)
    2. HW #2: Problems 17,19,23,24,28,32 (chapter 1, page 25)
    3. HW #3: Problems 36,37,43,45,46,51,52,55,56 (chapter 1, pages 29,38)
    4. HW #4: Problems 6,7,18,21 (chapter 3, pages 90,96,106)
    5. HW #5: Problems 69,72,75,76 (chapter 5, page 225)
    6. HW #6: Problems 15,21,22,24,26,27 (chapter 6, pages 245,252)
    7. HW #7: Problems 2,3,4,6 (chapter 8, page 317)
    8. HW #8: Problems 35,37,39,40,42,45,46 (chapter 8, page 351)
    9. HW #9: Problems 9,10,12,13,14,15,16 (chapter 8, page 323)
    10. HW #10: Problems (see handout)
    11. HW #11: Problems 27,28,29,31 (chapter 8, page 335)
    12. HW #12: Problems 2,4,5,7,8,10,11 (chapter 9, page 377)
    13. HW #13: Problems 24,25,26,28 (chapter 9, p.390)
    14. HW #14: Problems 40,41,42,44,46,47,49 (chapter 9, p.405)
    15. HW #15: Problems
    16. HW #16: Problems
    17. HW #17: Problems
    18. HW #18: Problems
    19. HW #19: Problems
    20. HW #20: Problems
    21. HW #21: Problems
    22. HW #22: Problems
    23. HW #23: Problems
    24. HW #24: Problems
    25. HW #25: Problems
    26. HW #26: Special Assignment: See handout.
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