STAT 453/553 STATISTICAL INFERENCE
Department of Mathematics and Statistics, UNM
Spring Semester 2016
INSTRUCTOR
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Office: 314 SMLC Building |
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email:ghuerta AT math DOT unm DOT edu |
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Class Time: Tue-Thurs 14:00-15:15. |
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Classroom: Collaborative Teaching and Learning Building (CTLB) 210. |
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Office Hours: T 12:00-1:00. Th 12:30-1.45pm, TR: 15:30-16:30 (for 15.30 only if I don't have a faculty meeting/seminar). By appointment for other times or days. |
INSTRUCTOR'S DESCRIPTION
The goal of this course is to give an introduction to the theory (and mathematics) of statistical inference. The first part of the course will discuss issues about random sampling, likelihood and sufficiency. The second part will discuss aspects on point estimation and hypothesis testing. The final part of the course will address confidence intervals and a brief introduction to asymptotic evaluations. The approach of this course is unified in the sense that will try to discuss concepts from the 3 main standpoints of statistical inference: frequentist, likelihood and bayesian. The course material along with Stat 461/561 are the basis for In-class portion of the Statistics qualifying exam.
CATALOG'S DESCRIPTION
Transformations of univariate and multivariate distributions to obtain the special distributions important in statistics. Concepts of estimation and hypothesis testing in both large and small samples with emphasis on the statistical properties of the more commonly used procedures, including Students t-tests, F-tests and chi-square tests. Confidence intervals. Performance of procedures under non-standard conditions (i.e., robustness).
PREREQUISITE
Stat 461/561: Probability (offered in the Fall). For Stat 443/553 its important to have a good understanding of basic Probability, probability distributions, expectations, variances and moments in general. Also some good familiarity with joint distributions, conditional and marginal distributions is required.
TEXTBOOK
Casella, G. and Berger, R.L. (2001) Statistical Inference. 2ed. Duxbury Press. (C&B, main text)
ADDITIONAL REFERENCE
Young, G. A. and Smith, R.L. (2010) Essentials of Statistical Inference. Cambridge University Press. (to support or complement material in Casella and Berger)
TOPICS
Chapter 5: Random samples and related concepts (mostly review).
Chapter 5: Convergence and generating random samples (review).
Chapter 6: Sufficiency, ancillary and completeness. The likelihood principle.
Chapter 7: Point estimation: Methods and properties of estimators.
Chapter 8: Hypothesis Testing: Methods for finding and evaluating tests.
Chapter 9: Interval estimation: Methods for finding and evaluating interval estimators.
Chapter 10: Asymptotic Evaluations
MY CLASS NOTES (based on the Casella and Berger book)
My Chapter 5 notes
My Chapter 6 notes
My Chapter 7 notes Part I
My Chapter 7 notes Part II
My Chapter 8 notes
GRADING
The grading will be based on a midterm exam, a final exam and quizzes. I plan to give a quiz roughly ever two weeks with a first quiz on January 28th and then one on February 11th. Each of the exams is worth 35% of the final grade. The quizzes are worth 30% of the final grade, there will be about 7-8 quizzes of about 15-20 minutes each during class. I have a policy of no make-up tests or quizzes. Only in the case of an emergency that that can be fully documented through a medical or police report, I will consider rescheduling an exam at an alternative date. Exercises from the textbook and other sources will be assigned regularly as Homework (HW). HW will not be graded but I highly encourage you to do it, since exam or quizzes problems can be taken out from HW. I will post a list of HW exercises through this webpage or our UNM learn webpage. I highly encourage you to work the HW problems in groups. The more you work on exercises from the text assigned or not assigned or from other sources, the more you will be prepared for the exams.
TEST DATES
Midterm: Thursday, March 10. Will cover material up to the class of March 8. review
Final exam: Tuesday May 10th, 10:00am-12:00pm in our regular classroom. Review for Final
HOMEWORKS (to be revised)
HW1: Exercises from Chapter 5 (C&B): 5.4, 5.15, 5.16, 5.24, 5.31, 5.35, 5,39, 5.40, 5.49, 5.50, 5.52, 5.56
HW2: Exercises from Chapter 6 (C&B): 6.6, 6.12, 6.15, 6.18, 6.21, 6.30, 6.34, 6.36
HW3: Exercises from Chapter 7 (C&B): 7.1, 7.8, 7.10, 7.11, 7.12, 7.19, 7.20, 7.24, 7.38,7.47,7.49,7.58
HW4: Exercises from Chapter 8 (C&B): 8.8a (only part (a) for this problem.),8.10,8.14,8.16,8.17, 8.18,8.22
HW5: Exercises from Chapter 9 (C&B): 9.10,9.13,9.17,9.23,9.26,9.39
This is a minimum list of problems you should work on. The more problems you work on, the better prepared you will be specially for the in-class quals. Solutions
to selected problems are available here. These are previous semesters so if you have questions, please let me know.
SolsCH6-2(and some of 7)
SolsCH7-8-9
UNM POLICY ON DISABILITIES
Qualified students with disabilities needing appropriate academic adjustments should contact me to ensure your needs are met in a timely manner.