**Course: Math 408, Mathematical Statistics, Fall 2021**

**Prerequisite:** Math 407, Probability Theory.

**Course Content:** Principles for testing hypotheses and estimation, confidence intervals, methods of moments, maximum likelihood, information inequality, likelihood ratio tests, goodness of fit and nonparametric methods.

*Last update:* 16 August 2021

Safety Protocols

- For updated information on safety protocols in the classroom, see here, here and here.
- If you are feeling sick, do NOT come to class. Follow the quarantine/testing protocols in the above links.
- In class, everyone must be wearing a face mask, such as a cloth mask, surgical mask, or N95 mask. A plastic face shield is NOT a face mask. If you are not wearing a face mask, you should not be in the classroom.
- Eating food is NOT allowed during class.
- There is a zoom link posted on blackboard in case hybrid teaching (a classroom lecture with camera/microphone) becomes necessary. The classroom is equipped with a camera/microphone, and I will try to get them working the first week of class.

**Instructor:** Steven Heilman, stevenmheilman(@-symbol)gmail.com

**Office Hours:** Tuesdays, 9AM-11AM, on zoom [link posted on blackboard]

**Lecture Meeting Time/Location:** Mondays, Wednesdays, and Fridays, 1PM-150PM, THH 114

**TA:** Andrew Lowy, lowya(@-symbol)usc.edu

**TA Office Hours:** Held in the Math Center, with schedule provided at that link.

**Discussion Section Meeting Time/Location**:

- 39520, Tuesdays and Thursdays, 12PM-1250PM, GFS 108
- 39521, Tuesdays and Thursdays, 1PM-150PM, GFS 108

**Textbook: **The following textbook is recommended but **not required**.

Rice, __Mathematical Statistics & Data Analysis__.

**Exam 1**: Monday, September 27, 1PM-150PM, THH 114

**Exam 2**: Friday, November 5, 1PM-150PM, THH 114

**Final Exam**: Wednesday, December 15, 11AM-1PM, Location TBD

**Other Resources:** Supplemental Problems from the textbook. An introduction to mathematical arguments, Michael Hutchings, An Introduction to Proofs, How to Write Mathematical Arguments

**Email Policy:**

- My email address for this course is stevenmheilman@gmail.com
- It is your responsibility to make sure you are receiving emails from stevenmheilman@gmail.com , and they are not being sent to your spam folder.
- Do NOT email me with questions that can be answered from this syllabus.

**Exam Procedures**: Students must bring their USCID cards to the midterms and to the final exam. Phones must be turned off. Cheating on an exam results in a score of zero on that exam. Exams can be regraded at most 15 days after the date of the exam. This policy extends to homeworks as well. All students are expected to be familiar with the USC Student Conduct Code. (See also here.)

Accessibility Services: If you are registered with accessibility services, I would be happy to discuss this at the beginning of the course. Any student requesting accommodations based on a disability is required to register with Accessibility Services (OSAS) each semester. A letter of verification for approved accommodations can be obtained from OSAS. Please be sure the letter is delivered to me as early in the semester as possible. OSAS is located in 301 STU and is open 8:30am-5:00pm, Monday through Friday.

https://osas.usc.edu/

213-740-0776 (phone)

213-740-6948 (TDD only)

213-740-8216 (fax)

OSASFrontDesk@usc.edu

Discrimination, sexual assault, and harassment are not tolerated by the university. You are encouraged to report any incidents to the *Office of Equity and Diversity* http://equity.usc.edu/ or to the *Department of Public Safety* http://capsnet.usc.edu/department/department-public-safety/online-forms/contact-us. This is important for the safety whole USC community. Another member of the university community - such as a friend, classmate, advisor, or faculty member - can help initiate the report, or can initiate the report on behalf of another person. *The Center for Women and Men* http://www.usc.edu/student-affairs/cwm/ provides 24/7 confidential support, and the sexual assault resource center webpage sarc@usc.edu describes reporting options and other resources.

**Exam Resources**: Some past 408 exams appear here, near the bottom of the page. Some practice exams for a course similar to ours appear here, here, and here

**Homework Policy**:

- Homeworks are
**due at 12PM noon Thursdays**, i.e. at the beginning of the first discussion session on Thursdays. - Homeworks are submitted in blackboard, under the "Assignments" tab. You are allowed unlimited submission "attempts" for an assignment, but only the last submission will be graded. To avoid internet issues, I recommend making your first submission of an assignment well in advance of the deadline.
- Homeworks should be submitted as single PDF documents. One way to create a PDF document from paper homework assignments is the freely available Adode Scan App
- Late homework is
**not accepted**. - If you still want to turn in your homework late, then the number of minutes late divided by ten will be deducted from the homework score. The exact deduction and rounding procedure is not guaranteed to be accurate.
- The
**single lowest**homework score will be dropped. This policy is meant to account for illnesses, emergencies, dropped internet connections, etc. - You may not use the internet to try to find answers to homework problems.
- Do not submit homework via email.
- Collaboration on homeworks is allowed and encouraged.
- All homework assignments must be written by you, i.e. you cannot copy someone else`s solution verbatim.

**Quiz Policy**

- There will be several quizzes throughout the semester, as listed in the schedule below, roughly every other week. One week before the quiz occurs, a list of quiz problems will be posted on the course website. The quiz will have a few problems similar or identical to the posted list of problems.
- The
**single lowest**quiz score will be dropped. This policy is meant to account for illnesses, emergencies, etc. - Quizzes will be administered in your discussion section on Thursday. Each quiz should last about 10-15 minutes.
- No notes, no books, no calculators, etc. will be allowed during the quizzes.

**Grading Policy:**

- The final course grade is weighted as the larger of the following two schemes.
- Scheme 1: class participation (3%), homework (11%), quizzes (11%), the first midterm (20%), the second midterm (20%), and the final (35%).
- Scheme 2: class participation (3%), homework (11%), quizzes (11%), the largest midterm grade (30%), and the final (45%).

- If you cannot attend one of the exams, you must notify me within the first two weeks of the start of the quarter. Later requests for rescheduling will most likely be denied.
- Class participation is not the same as attendance. I will never explicitly take attendance, but I will notice if someone is frequently absent. Things that increase your class participation grade include: asking good questions, paying attention in class, showing up on time or early to class, etc. Things that decrease your class participation grade include: excessive talking or disruptions during class, frequent absences, excessive texting/smartphone usage in class, frequent tardiness, etc.
- You must take the final exam to pass the course.

Tentative Schedule: (This schedule may change slightly during the course.)

Week | Monday | Tuesday | Wednesday | Thursday | Friday |

1 | Aug 23: Review of Probability | Aug 24 | Aug 25: 5.3, Review of Probability | Aug 26: Homework 1 due | Aug 27: 6.2, 6.3, Review of Probability |

2 | Aug 30: 7.3, Review of Probability | Aug 31 | Sep 1: 8.1, 8.2, Parameter Estimation | Sep 2: Quiz 1 | Sep 3: 8.3, Parameter Estimation |

3 | Sep 6: No class | Sep 7 | Sep 8: 8.4, Method of Moments | Sep 9: Homework 2 due | Sep 10: 8.5, Maximum Likelihood Estimation |

4 | Sep 13: 8.6, Efficiency, Cramer-Rao | Sep 14 | Sep 15: 8.7, Sufficiency, Rao-Blackwell | Sep 16: Quiz 2 | Sep 17: 9.1, 9.2, Hypothesis Testing |

5 | Sep 20: 9.3, Neyman-Pearson Lemma | Sep 21 | Sep 22: 9.4, Confidence Intervals | Sep 23: Homework 3 due | Sep 24: 9.5, 9.6, Likelihood Ratio Tests |

6 | Sep 27: Exam 1 | Sep 28 | Sep 29: 10.6, Boxplots | Sep 30: Quiz 3 | Oct 1: 11.2, Comparing Two Independent Samples |

7 | Oct 4: 11.3, Comparing Paired Samples | Oct 5 | Oct 6: 11.4, Experimental Design | Oct 7: Homework 4 due | Oct 8: 12.2, Analysis of Variance |

8 | Oct 11: 12.2.2, Multiple Comparisons | Oct 12 | Oct 13: 12.2.3, Kruskal-Willis | Oct 14: No class | Oct 15: No class |

9 | Oct 18: 12.3, Two-Way Layout | Oct 19 | Oct 20: 12.3, Two-Way Layout | Oct 21: Quiz 4 | Oct 22: 13.2, 13.3, Analysis of Categorical Data |

10 | Oct 25: 13.4, 13.5, Chi-Square Test | Oct 26 | Oct 27: 13.5, 13.6, Matched Pairs, Odds Ratio | Oct 28: Homework 5 due | Oct 29: 14.2, Linear Regression |

11 | Nov 1: 14.2, Linear Regression | Nov 2 | Nov 3: 14.2, Linear Regression | Nov 4: No homework due | Nov 5: Exam 2 |

12 | Nov 8: 14.3, 14.4, Least Squares | Nov 9 | Nov 10: 14.3, 14.4, Least Squares | Nov 11: Quiz 5 | Nov 12: 14.5, Multiple Linear Regression |

13 | Nov 15: 14.6, Conditional Inference | Nov 16 | Nov 17: 15.2, Decision Theory | Nov 18: Homework 6 due | Nov 19: 15.2, Decision Theory |

14 | Nov 22: 15.3.1, Subjectivist Perspective | Nov 23 | Nov 24: No class | Nov 25: No class | Nov 26: No class |

15 | Nov 29: 15.3.2, Subjectivist Perspective | Nov 30 | Dec 1: Review of course | Dec 2: Quiz 6 | Dec 3: Review of course |

**Advice on succeeding in a math class:**

- Review the relevant course material before you come to lecture. Consider reviewing course material a week or two before the semester starts.
- When reading mathematics, use a pencil and paper to sketch the calculations that are performed by the author.
- Come to class with questions, so you can get more out of the lecture. Also, finish your homework at least two days before it is due, to alleviate deadline stress.
- Write a rough draft and a separate final draft for your homework. This procedure will help you catch mistakes.
- If you are having difficulty with the material or a particular homework problem, review Polya's Problem Solving Strategies, and come to office hours.

**Homework**

**Homework .tex files**

**Quiz Problems**

**Exam Solutions**

**Supplementary Notes**