# Stat 640: Advanced Statistical Theory

Department of Statistics and Biostatistics, CSU East Bay

**Fall 2023:**

**MS Exam Preparation Spring 2024:**

- I was asked about how to access the solution for the Stat. 640 Fall 2023 Final Exam. The posted materials from Canvas are no longer available. I have posted the file here on the class website.
- Stat640_final.pdf Please note that the year was wong on the file, it was 2022, but this was the final for 2023.
- Stat640_final_solution.pdf

**Finals Week:**

- The class final will be next week on Wednesday. Stat640-01 3-5pm, Stat640-02 8-10pm.
- The final for Section 1 will be given on campus in the classroom. All students in Section 1 will take the exam at the same time in the classroom. If you are sick or have a conflict, please contact me to make arrangements to take the exam. Everyone is expected to be academically honest when taking the exam.
- The final for Section 2 will be given online. The exam will be posted on Canvas at 8pm on Wednesday and will be due at 10:15pm on Wednesday. You will have 2 hours to complete the exam once you start it. This is an online class and everyone is expected to be academically honest when taking the exam.
- The final will cover topics covered since the last Midterm.
**Topic include:**Estimation, MME, MLE, Confidence Intervals, Hypothesis Testing, Parametric Bootstrap, Large Sample Theory of MLEs, Fisher’s Information, Asymptotic Variance, Likelihood Ratio Test, MP test, UMP tests, UMPU tests, Size, Power, and Generalized Likelihood Ratio Tests. There will be 4 problems on the final. 1. MME and/MLE 2. Fisher’s Information, AV, 3. Likelihood Ratio Test, 4. GLR test. - The final will be open book, open notes, and open computer for the book. You may use any printed material, notes, and handouts. You may
**not**use the internet or communicate with anyone else during the exam.

**Week 15:**

**Quiz:**Solution in class on Monday.**Topics:**Large Sample Theory of GLR Tests, Power, Sample Size, and Sufficient Statistics**Handouts:**Confidence, Power, Likelihood Ratio Tests, and the distribution of the p-value**Final:**Next week is finals week.- All work should be completed this week by Friday.

**Week 14:**

**Quiz 3:**Quiz 3 will be given as a take-home quiz on Wednesday next week and will be due after the Thanksgiving break. Posted in Canvas, Files > quiz03. Due Friday December 1.**Homework:**Assignment 10 has been posted.**Topics:**Hypothesis Testing, MLR, UMP Tests, UMPU Tests, GLR Tests, Review**Handouts:**See the posted handouts related to the Nonparameteric Bootstrap.

**Week 13:**

**Homework Solutions:**The solutions to Homework 8 and 9 (not complete) have been posted in Canvas under Files.**Topics:**Hypothesis Testing, Neyman-Person Lemma**Handouts:**The handout for Week 13 have been posted. The handout summarizes the discussion about the Large Sample Theory of MLEs.

**Week 12:**

**Topics:**Plotting the fitted model (see Handouts Week 11), Bootstrap, CRLB**Homework:**Homework 9 has been posted.**Homework Solutions:**The solutions to Homework 7 have been posted in Canvas under Files.**Quiz 2 and Midterm Solutions:**The solutions to Quiz 2 and Midterm 2 have been posted in Canvas under Files.**Quiz 3:**Quiz 3 will be given as a take-home quiz on Wednesday next week and will be due after the Thanksgiving break.

**Week 11:**

**Topics:**Hardy-Weinberg Law, Bootstrap, “irregular estimation”, Large Sample Theory of the MLE, \(AV(\hat{\theta})\)**Midterm:**Midterm 2 will be returned on Wednesday.**Homework:**Homework 8 has been posted.**Quiz:**R code has been posted for Quiz 2 solution Canvas.

**Week 10:**

**Midterm:**Midterm 2 will be in class next week on Monday.**Topics:**MLE**Homework:**Homework 7 has been posted.**Due date extended.**

Hello everyone,

We have our Midterm 2 tomorrow during class.

If you are sick or not feeling well or suspect you might be sick, you are encouraged to reach out to the instructor to make arrangements to take the Midterm 2 online.

For everyone else, if you would like to request taking the Midterm 2 online, feel free to ask.

As a reminder, everyone’s work is to be your own work and you are to follow the University Academic Dishonesty Policy.

Prof. Suess

**Week 9:**

**Topics:**MLE**Quiz:**Quiz 2 will be on Monday at the start of class.**Midterm:**Midterm 2 will be in class next week on Monday.

**Week 8:**

**Topics:**\(\bar{X}_n\), \(S^2_n\), Point/Parameter Estimation, Interval Estimation, Hypothesis Testing, MME**Assignment:**Homework 7 has been posted.**Due date extended.****Homework Solutions:**The solutions to Homework 5 and 6 have been posted in Canvas under Files.**Quiz:**Quiz 2 will be next week on Monday. The quiz will be given during the first 30 minutes of the class period on Monday and will be collected or is due in Canvas 15 minutes later. For those that cannot make it to class because of illness or other arrangements with the instructor the quiz will be available on Canvas > Files. If you are sick or receive extra time, you need to contact the instructor before the start of the quiz to make arranges for taking the quiz.**Topics include:**Expectation and Variance, Limit Theorems, and Derived Distributions.**Review:**To prepare for the quiz, review the problems in Homework 4, 5, and 6.

**Week 7:**

**Topics:**Convergence in Distribution, Continuity Thm, CLT for Poisson, Prediction, Derived Distributions.**Assignment:**Homework 6 has been posted.**Homework Solutions:**The solution to Homework04 has been posted, except for the Exercises.**Midterm Solution:**The solution to Midterm01 has been posted.

**Week 6:**

**Topics:**Discuss topics related to Expectation, Variance, Covariance, and Correlation.

**Midterm:**Questions on Monday.- Homework 3 solutions posted in Canvas.
**Corrected:**Pareto distribution is now correct. **Assignment:**Homework 5 has been posted.- LaTeX math symbols to use in R Quarto Notebooks:

**Week 5:**

**Announcement:**Class on Monday will be online for the 2pm section.**Midterm:**The first midterm will be take-home. The midterm will be available on Monday next week and due at the end of the week.**Topics:**Box-Muller algorithm for normal random number generation. Order Statistics, Minimum and Maximum, Quantiles.**Assignment:**Homework 4 has been posted.

**Week 4:**

**Updated:**The Dates webpage for the quizzes and midterms has been updated. No dates have been changed, but the day of the week has been corrected.

**Quiz:**Because of the mistake on the Dates webpage, the first quiz will be take-home. The quiz will be made available on Monday and will be due end of the day on Wednesday.**Topics to include:**Probability Models, Independence, Plotting discrete and continuous probability models, Functions of Random Variables, Inverse CDF Method, Simulation of random values. The quiz is available on Canvas > Files.**Topics:**Jointly distributed random variables, Order Statistics.**Homework Solutions:**The solutions to Homework 1 have been posted in Canvas under Files. If you are having problems Rendering your R Quarto Notebook to .pdf please come to office hours to see if we can fix the issue with your installed R packages. If you cannot Render to .pdf, try to Render to .docx, that might work. If that does not work, I have recently learned that there is a way to Render to a .html file that is self-contained and that can be uploaded to Canvas. To Render a self-contained R Quarto Notebook the YAML header needs to be modified, see the following YouTube video: How to create self-contained HTML files in Quarto**Homework Guidelines:**homework_guidelines.pdf**Assignment:**Homework 3 has been posted.

**Week 3:**

**Topics:**Functions of Random Variables. Proposition C and Proposition D. Inverse CDF Method for generating random numbers. Joint Distributions and Conditional Distributions.**Assignment:**Homework 2 has been posted.

**Week 2:**

- In class we will start with a few Probability Examples that use Independence. See the Handouts link.
**Topics:**Probability Simulation, Random Variables, Probability Models, Simulation of Random Values.- In class we will start with a discussion of Probability Models that can be described using an
*urn*model. **Homework submission:**should be done through**Canvas**. Your papers should be submitted in the order assigned. Your name should appear on each page. I would suggest starting each problem at the top of a new page so it is clear to me which problem you are working on.**Assignment:**Homework 1 has been posted.

**Week 1:**

- In class we will go over the syllabus.
- The classroom technology will be tested.
- The lectures will be available through Zoom during the class times and the recording will be posted in
**Canvas**.

**Week 0:**

- Welcome to Statistics 640.