Time and place: MWF 09:40-10:30, Lockett 240
Instructor: James Madden, 213 Prescott Hall, madden@math.lsu.edu, (225)-978-3525 (cell)
Textbook: Casella and Berger: Statistical Inference 2nd ed. (This book is available from on-line dealers at a reasonable price.)
Goal: This course deals with the mathematical principles that underlie and justify the most common basic techniques of statistical inference. The focus is not on the development and use of techniques for dealing with complex statistical problems, but on understanding the most commonly used statistical methods clearly and rigorously.
Grading: Homework 25%. Friday quizzes 25%. Midterm and final 50%.
| week | mm/dd | D | Topic | Assignment | Notes/resources |
1 |
08/23 | M | Introduction | Announcements Presentation (needs Mathematica) |
|
| 08/25 | W | Probability review I | Read: p. 27-29, p. 34-37, p.86, p. 89, p. 92, p. 102, Sec. 2.2. Hand in 08/30: (p. 76) 2.4, 2.13, 2.15, 2.20, compute the mgf of a normal(0,1) r.v. |
copy of exercises (from text) | |
| 08/27 | F | Quiz (binomial dist.); Probability review II: Moment generating functions. |
Read: Sec. 2.3, pages 182-184 (independence). Hand in 08/30: (p. 80) 2.33 |
notes (Philos. Intro. to Stat. Inf.) answers to quiz 1 |
|
2 |
08/30 | M | Sampling statistics | notes | |
| 09/01 | W | Sample mean and variance | Hand in 09/08: problem in notes. | notes | |
| 09/03 | F | Sampling the normal, I. Sums and averages of independent normal variables | Hand in 09/08: xeroxed problems: 26, 32, 34; find and do the one other of the problems from 26-36 that is directly related to the new material of today. Read: section 5.2. | quiz notes |
|
3 |
09/06 | M | Holiday | --- | --- |
| 09/08 | W | Sampling the normal, II. Sample variance. | Hand in 09/15 (revised date): The problems in the lecture notes for 09/08. | notes | |
| 09/10 | F | Change of variables and transformations of random variables. | Hand in 09/15: 4.20 (page 194) | quiz notes |
|
4 |
09/13 | M | Sampling the normal, III. Proofs concluded. | Hand in 09/17: 5.6 (page 256). Read: 5.3. | see notes from 09/08 |
| 09/15 | W | The gamma and chi-squared distributions | Hand in 09/20: the problems in the notes. | notes | |
| 09/17 | F | Student's t and Snedecor's F | Hand in 09/22: the problems in the notes | quiz notes |
|
5 |
09/20 | M | Sufficient statistics I | notes | |
| 09/22 | W | Sufficient statistics II | Hand in 09/27: problems in notes | notes | |
| 09/24 | F | Review | Hand in 09/27: problem 6.7 (page 300) Read: the handout |
quiz wikipedia on sufficiency |
|
6 |
09/27 | M | Liklihood and the MLE | -- | notes |
| 09/29 | W | MLE may be biased | See notes | notes | |
| 10/01 | F | Poisson MLE | We discussed the quiz | quiz with commentary | |
7 |
10/04 | M | Mean Squared Error | Homework (9/24) due date revised; Get Homework Hints. |
notes |
| 10/06 | W | Misc. Problems | |||
| 10/08 | F | Homework review | Notes to Review for Midterm | ||
8 |
10/11 | M | Review for Midterm | ||
| 10/13 | W | Midterm Exam | Students will receive a "curved score" (i.e., more points) if they work the exam problems at home and hand them in on Friday. | ||
| 10/15 | F | discussion of exam | |||
9 |
10/18 | M | no class | ||
| 10/20 | W | Bayes Estimators | notes | ||
| 10/21 | F | Fall Break | |||
10 |
10/25 | M | Hypothesis Testing I | notes | |
| 10/27 | W | no class | |||
| 10/29 | F | Hypothesis Testing II | notes | ||
11 |
11/01 | M | Hypothesis Testing III | notes | |
| 11/03 | W | Neyman-Pearson Lemma | notes | ||
| 11/05 | F | Neyman-Pearson Lemma | see notes from 11/03 | ||
12 |
11/08 | M | Examples | Problem 8.19 | |
| 11/10 | W | Examples | notes | ||
| 11/12 | F | Problems | (end-of-chapter problems from Rice) | ||
13 |
11/15 | M | Confidence Intervals | ||
| 11/17 | W | Confidence Intervals | notes for 11/15 and 11/17 | ||
| 11/19 | F | Confidence Intervals | |||
14 |
11/22 | M | ANOVA | ||
| 11/24 | W | ANOVA | Mathematica notebooks: Normal, StudentT, FRatio |
notes for 11/22 and 11/24 | |
| 11/26 | F | Vacation | |||
15 |
11/29 | M | Rice, Ch. 9 problems: 13-18, 19-24. Homework: 13, 17, 19 (will discuss Wedn.) | notes (answers to take-home) | |
| 12/01 | W | Mathematica notebook: Investigating the F distribution |
notes (problems 13, 17, 19) | ||
| 12/03 | F | (last class) | |||
| 12/09 | Th | FINAL EXAM | In regualr room, 10AM--NOON | ||