Math 476: Statistics and Math 563: Mathematical Statistics
Lecture schedule
You are expected to cover the assigned readings before coming to the lecture. This will help you follow the course and organize your notes. In the reading schedule below, "WMS" refers to Wackerly, Mendhall, Scheaffer, Mathematical Statistics with Applications, and "Shao" refers to the complementary text for math 563. (Students in math 476 are not required to read/use Shao.)| Dates | Tentative topics covered | Assigned reading | Related homework |
| January 14&16 | Topic 1: What is statistical inference? Statistics and sampling distributions | WMS: Sections 1.4, 7.1-7.4. Shao: Sections 2.1.1, 2.2.1, 1.5.4, 1.5.5. |
This material is covered in problems from Homework 1, which is due 1/28. |
| January 21&23 | Topic 2: Estimation: point estimation basics. Bias. Goodness of a point estimator. |
WMS: 8.1-8.4. Shao: 2.4.1. (and the introduction to section 2.4.) |
Homework 2 due 2/4. |
| January 28&30 | Topic 3: Estimation: Conidence intervals and sample size. |
WMS: 8.5-8.9 Shao: 2.4.3. (and the introduction page to section 2.5.) |
Homework 3 due 2/11. |
| February 4&6 | Topic 3 (cont'd): Estimation: confidence intervals. Topic 4: Properties of point estimatros: efficincy, consistency. |
WMS: 8.9, 9.1-9.3 (and 9.4, time permitting) Shao: 2.2.2, 2.5.1. Rest of 2.5. 7.1. |
Homework 3 due 2/11 and Homework 4 due 2/18. |
| February 11&13 | Topic 4 (cont'd): Properties of point estimators:
sufficiency. MVUEs. Rao-Blackwell. Topic 5: Where do estimators come from? Methods of moments and maximum likelihood. |
WMS: 9.4-9.7 (and 9.8, time permitting) Shao: 3.1, 3.5.2, 4.4. |
Homework 4 due 2/18 and Homework 5 due 2/25. | February 18 | QUIZ 1: In class, one page of notes allowed. Chapters 8 and 9. | Homework sets 1 - 3. |
| February 18&20 | Topic 5 (cont'd): Computing MLEs and examples. Properties of Maximum likelihood estimators. [invariance, consistency, efficiency, asymptotic normality.] AND: review of Chapters 8 and 9. |
WMS: 9.7, 9.8, and references given in the book. |
Homework 5 due 2/25 |
| February 25&27 | Topic 6: Introduction to hypethesis testing: Elements of a statistical test; Common large-sample tests. |
WMS: 10.1-10.3 (Shao: none this week.) |
Homework 6 due 3/11 | March 6 | MIDTERM EXAM: In class, one page of notes allowed. | Chapters 7, 8 and 9. | Homework sets 1 - 5. |
| March 4 | Topic 6 (cont'd) Calculating Type II Error
probabilities and finding sample size for Z tests |
WMS: 10.4 and 10.5. (Shao: none this week.) |
Homework 6 due 3/11 |
| March 11&13 | Topic 7: p values. Small sample tests. (Hypothesis testing for variances - time permitting.) |
WMS: 10.6, 10.7, 10.8 (and 10.9, time permitting) (Shao: tbd) |
Homework 7 due 3/25 |
| March 17-21 | spring break | Catch up on reading! | |
| March 25&27 | Topic 8: Power of tests, Neyman-Pearson, Likelihood ratio tests. |
WMS: 10.10, 10.11, 10.12. |
Homework 8 due 4/1 |
| April 1&3 | Topic 9: Analysis of categorical data |
WMS: 14.1-14.4 (and 14.5 if time permits) (Shao: tbd) |
Homework 9 due 4/8 |
| April 8&10 | Topic 10: linear models. Linear statistical models, method of least squares, properites of LS estimators (simple linear regression). |
WMS: 11.1-11.4. |
Homework 10 due 4/15 |
| April 15&17 | Topic 11: Inferences concerning paramters of a linear model and predicting values using simple linear regression. |
WMS: 11.4(continued), 11.5-11.7 |
Homework 11 due 4/25 (extended to 4/28 as needed) |
April 22 | MIDTERM EXAM: In class, one page of notes allowed. | Chapters 10, 14, and beginning sectinos of 11. | Homework sets 6-10. |
| April 24 | Topic 12: Exact tests: exact p-value, non-asymptotic test. |
Haberman 1988, Bunea and Besag 2000, and furhter reference provided in class. |
No more homework. |
| April 29&31 | Topic 13: Correlation. Nonparamteric statistics. |
WMS: 11.8, 15.1-15.3. |
Just review everything for the final exam! |
Comprehensive Final Exam | WENESDAY, May 7th 2014, 2-4pm. |