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INTRODUCTION to MATHEMATICAL STATISTICS Fall 2014 Instructor: Dr Stephen Walker ([email protected])

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INTRODUCTION to MATHEMATICAL STATISTICS Fall 2014 Instructor: Dr Stephen Walker (S.G.Walker@Math.Utexas.Edu) M378K: INTRODUCTION TO MATHEMATICAL STATISTICS Fall 2014 Instructor: Dr Stephen Walker ([email protected]) 10.174 RLM Lectures: Monday & Wednesday & Friday, 11.00 to 12.00. Office hours: Monday and Wednesday, 9.00 to 10.30 Textbooks: Schaums's Outline of Statistics, Fourth Edition (Schaums's Outline Series). Murray Spiegel and Larry J. Stephens. Introduction to Mathematical Statistics, Fifth Edition (Wiley Series in Probability & Mathematical Statistics). Paul G. Hoel. Content: The course will be developed from the notion that Statistics is about performing operations on variables arising from distribution functions. The specific operations involve implementing tasks such as estimation, both point estimation and interval estimation, and hypothesis testing. Many of the concepts will be demonstrated on the normal distribution and more broadly the exponential family where properties of the procedures will be derived. Throughout, emphasis will be placed on the understanding of what the statistical goals are. Specific topics covered in some depth include hypothesis testing (e.g. likelihood ratio tests, most powerful tests); asymptotic analysis (the pinning down of procedures when sample sizes are large); nonparametric methods (no distributional assumptions are made in the quest for summaries); notions of sufficiency, multivariate analysis and a brief flirtation with Bayesian statistics. Prerequisites: Mathematics 362K. Class Notes: Notes for the lectures will provided on Canvas at the start of each week. Exams: There will be 2 exams; set approximately at 1/3 and 2/3 of the way during the course, and will be set during regular class, and the final exam. Assignments: A number of assignments will be set during the course. Grades: Grades for the course will be allocated as follows: 80% for the Exams and 20% for the Assignments. Tentative Schedule: Week Topic 1. Introduction to Statistics 2. The normal distribution and point estimation 3. The normal distribution, confidence intervals and hypothesis testing 4. Two sample tests (+Assignment 1) 5. The exponential family 6. Sufficiency (+Exam 1) 7. Linear models 8. Nonparametric methods (+Assignment 2) 9. Goodness of fit 10. Asymptotics 11. More on hypothesis testing (+Exam 2) 11. Bayesian methods 12. Sample size selection (+Assignment 3) 13. Method of moments 14. Estimation methods, e.g. EM algorithm (+Assignment 4) 15. Summary Accommodations: The University of Texas at Austin provides upon request appropriate academic accommodations for qualified students with disabilities. For more information, contact Services for Students with Disabilities at 471-6259 (voice) or 232-2937 (video phone) Honor Code: The core values of The University of Texas at Austin are learning, discovery, freedom, leadership, individual opportunity, and responsibility. Each member of the university is expected to uphold these values through integrity, honesty, trust, fairness, and respect toward peers and community. University policy on holy days: A student who misses classes or other required activities, including examinations, for the observance of a religious holy day should inform the instructor as far in advance of the absence as possible, so that arrangements can be made to complete an assignment within a reasonable time after the absence..
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