Fall 2022 - STAT 830 G100

Statistical Theory I (4)

Class Number: 4665

Delivery Method: In Person

Overview

  • Course Times + Location:

    Tu, Th 1:30 PM – 3:20 PM
    AQ 5039, Burnaby

  • Prerequisites:

    STAT 450 or permission of the instructor.

Description

CALENDAR DESCRIPTION:

The statistical theory that supports modern statistical methodologies. Distribution theory, methods for construction of tests, estimators, and confidence intervals with special attention to likelihood and Bayesian methods. Properties of the procedures including large sample theory will be considered. Consistency and asymptotic normality for maximum likelihood and related methods (e.g., estimating equations, quasi-likelihood), as well as hypothesis testing and p-values. Additional topics may include: nonparametric models, the bootstrap, causal inference, and simulation. Students with credit for STAT 801 may not take this course for further credit.

COURSE DETAILS:


Course Outline:

We will be discussing how to develop and evaluate statistical methods. We survey various general statistical techniques: prediction, forecasting, point and interval estimation, and hypothesis testing; we discuss how to assess how well a specific technique works in repeated sampling terms: forecast standard error, standard error of estimation, coverage probabilities, error rates; we consider optimality theory; throughout we examine trade-offs: bias versus variability, type I versus type II error rates, interval coverage versus precision or length, mechanistic versus empirical models, and others. The vision is that we use the techniques of probability to discuss inference in the face of uncertainty. I will start with inference and fill in background in probability as needed. Our focus is chapters 6 through 11 of the Larry Wasserman's text All of Statistics but I don't think you really need the text. It is available electronically through the library.

1. Probability: random variable, expectation, inequalities, and convergence
2. Inference: Parametric and nonparametric models, empirical distribution function, bootstrap, maximum likelihood and related methods, properties of MLEs and related methods, hypothesis testing and p-values, simulation, selected topics.

Course Details:

  • Lecture: This will be a standard in person lecture-based offering. During the pandemic I pre-recorded lectures which will be available on Canvas and on SFU’s Mediasite.
  • Website: There will be a variety of material available in Canvas I do not expect to be able to record the classroom presentations. My own website has lots of extras from older versions of the course.
  • Office Hours: I will be on campus every day in the fall and will hold office hours before the lectures.
  • Assignments: These play a modest role in evaluation and a big role in learning. They are harder than exams.
  • My presence on campus: every day except some Fridays.

Mode of Teaching:
  • Lectures: In person.
  • Tutorial: None
  • Midterm: in person on October 13.
  • Final exam: In person. Date: TBA.

Grading

  • Assignments 40%
  • Midterm 20%
  • Final exam 40%

NOTES:

Above grading is subject to change.

REQUIREMENTS:

Students will need to download and install R and I will encourage the use of RStudio. You should also install a working TeX version or be prepared to use something like Overleaf. These are all available on most computing platforms and are free in general for students.

Materials

MATERIALS + SUPPLIES:

Access to high-speed internet, webcam.

REQUIRED READING:

Textbook:

All Of Statistics: A Concise Course in Statistical Inference by Larry Wasserman. Publisher: Springer.

eBook: ISBN 978-0-387-21736-9
Softcover: ISBN 978-1-4419-2322-6
Harcover: ISBN 978-0-387-40272-7

RECOMMENDED READING:

Available in electronic form through lib.sfu.ca.  I won't be requiring this text but the notes follow it and refer to it from time to time.

Here is a list of texts which are available in the library and which cover many of the ideas I want to touch on.

Polansky, Alan M. Introduction to Statistical Limit Theory. (2011).
Abramovich, Felix and Ritov, Ya'acov. Statistical Theory: A Concise Introduction. (2013).
Silvey, S. D. Statistical Inference. (1975).
DasGupta, Anirban. Asymptotic Theory of Statistics and Probability. (2008).

Graduate Studies Notes:

Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

SFU’s Academic Integrity web site http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating.  Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the University community.  Academic dishonesty, in whatever form, is ultimately destructive of the values of the University. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the University. http://www.sfu.ca/policies/gazette/student/s10-01.html