Stat 640: Advanced Statistical Theory
Department of Statistics and Data Science, CSU East Bay
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 legitimate verifiable conflict, please contact me by email this week to make alternative arrangements to take the exam. Everyone is expected to be academically honest when taking the exam.
- The final for Section 2 will be given on campus in the classroom or on Zoom. All students in Section 2 will take the exam at the same time in the classroom or on Zoom. If you are sick or have a legitimate verifiable conflict, please contact me by email this week to make arrangements to take the exam. 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.
- MME and/MLE,
- Fisher’s Information, AV, Confidence Intervals,
- Likelihood Ratio Test,
- GLR test.
- The final will be closed book, open notes 15 page of your own notes, closed computer, closed internet, and no phone can be used. You may not use the internet or communicate with anyone else during the exam.
Fall 2025:
- 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
- The Homework solutions for the remaining assignments have been posted in Canvas > Files > Homework Solutions. Corrections: Homework 9 Solution is mislabeled as Homework 3. Homework 10 Solution is mislabeled as Homework 2. Please disregard the labels.
- The solutions to Quiz 3 will be posted in Canvas > Files > Quiz Solutions.
- Final: Next week is finals week.
- All work should be completed this week by Friday.
- Spotlight Book: An Introduction to Bayesian Thinking
Week 14:
- Quiz 3: Quiz 3 will be given as a take-home quiz on Wednesday and will be due after the Thanksgiving break. Posted in Canvas, Files > quiz03. Due Friday December 5.
- Homework: Assignment 10 has been posted.
- Topics: Hypothesis Testing, MLR, UMP Tests, UMPU Tests, GLR Tests
- Handouts: See the posted handouts related to the CRLB and Nonparameteric Bootstrap.
- Handouts: Confidence, Power, Likelihood Ratio Tests, and the distribution of the p-value
Week 13:
- Homework Solutions: The solutions to Homework 7 has been posted in Canvas under Files.
- Midterm 2 Take-home Solutions: The solutions to the Mideterm02 Take-home have been posted in Canvas. Some people have received mesages in Canvas about completely their submission, submit your .qmd and/or correct your formating to be self-contained.
- Topics: Large Sample Theory of the MLE, \(AV(\hat{\theta})\), CRLB, 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.
- Spotlight News:
Week 12:
- Topics: MME, Bootstrap, Large Sample Theory of the MLE, \(AV(\hat{\theta})\), Plotting the fitted model (see Handouts Week 12), CRLB
- Homework: Homework 9 has been posted.
- Quiz 2: The solutions to Quiz 2 has been posted in Canvas under Files.
- Midterm: Take-home Midterm 2 due November 7. Question 8 independent samples or paired samples?
Week 11:
- Topics: Likelihood, MLE, “irregular estimation”
- Midterm: Take-home Midterm 2 will be posted on Wednesday. Due November 7.
- Assignment: Homework08 has been posted.
- Homework: Homework07 due date extended.
- Quiz: R code has been posted for Quiz 2 solution Canvas.
- Reference: A First Course on Statistical Inference 5.1 The pivotal quantity method
Week 10:
- Quiz: Quiz 2 will be on Wednesday at the start of class.
- Topics: Prediction, Sampling, Point/Parameter Estimation, Interval Estimation, Hypothesis Testing.
- Assignment: Homework07 has been posted.
- Homework Solutions: The solutions to Homework 4, 5 and 6 have been posted in Canvas under Files.
- Quiz: Quiz 2 will be on Wednesday. The quiz will be given during the first 30 minutes of the class period on Wednesday. Topics include: Expectation and Variance, Chebyshev’s Inequality, Limit Theorems, and Derived Distributions. Review: To prepare for the quiz, review the problems in Homework 4, 5, and 6.
Week 9:
- Topics: CLT for Poisson, Prediction, \(\bar{X}_n\), \(S^2_n\), Derived Distributions.
- Assignment: Homework06 has been posted.
Week 8:
- Topics: Convergence in Distribution, Continuity Theorem.
- Assignment: Homework05 has been posted.
- Updated: The Dates webpage for the quizzes and midterms has been updated.
- Midterm Solution: The solution to Midterm01 has been posted.
Week 7:
- Topics: Discuss topics related to Expectation, Variance, Covariance, and Correlation.
- Midterm: Midterm 1 is in class on Wednesday.
- Homework Solutions: The solution to Homework03 has been posted.
Week 6:
- Topics: Discuss topics related to Expectation, Variance, Covariance, and Correlation.
- Assignment: Homework 4 has been posted.
- Spotlight Youtube Videos: See Week 5: for the videos related to the Normal distribution.
- Quarto, LaTeX: LaTeX math symbols to use in R Quarto Notebooks:
Week 5:
- Quiz: The first Quiz will be next week on Wednesday at the start of class. Topics to include: Probability Models, Independence, Plotting discrete and continuous probability models, Functions of Random Variables, Inverse CDF Method, Simulation of random values. You may prepare 4 pages of handwritten notes that you may use during the quiz. You will need to bring a calculator. No other electronic devices are allowed.
- Topics: Box-Muller algorithm for normal random number generation. Order Statistics, Minimum and Maximum, Quantiles.
Week 4:
- Updated: The Dates webpage for the quizzes and midterms has been updated.
- Topics: Joint Distributions and Conditional Distributions, Order Statistics.
- Homework Guidelines: homework_guidelines.pdf
- Assignment: Homework 3 has been posted.
Week 3:
- Holiday: No class on Monday, September 1, 2025 (Labor Day).
- Topics: Functions of Random Variables. Proposition C and Proposition D. Inverse CDF Method for generating random numbers.
- Assignment: Homework01 AI, Homework 2, Homework02 AI have 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: Your handwritten homework solutions should be done through Canvas. Your papers should be scanned into a .pdf file and 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. Your R code should be completed in an R Quarto Notebook Rendered to a .html file and submitted through Canvas, submit both the .qmd file and the .html file.
- 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.