Simon Fraser University
Engaging the World

Course Outlines

Fall 2025 - STAT 450 D100

Statistical Theory (3)

Class Number: 7101

Delivery Method: In Person

Overview

  • Course Times + Location:

    Sep 3 – Dec 2, 2025: Mon, 10:30 a.m.–12:20 p.m.
    Burnaby

    Sep 3 – Dec 2, 2025: Wed, 10:30–11:20 a.m.
    Burnaby

  • Exam Times + Location:

    Dec 7, 2025
    Sun, 12:00–3:00 p.m.
    Burnaby

  • Prerequisites:

    STAT 330 with a minimum grade of C-.

Description

CALENDAR DESCRIPTION:

Distribution theory, methods for constructing tests, estimators, and confidence intervals with special attention to likelihood methods. Properties of the procedures including large sample theory. Quantitative.

COURSE DETAILS:


Additional note regarding the pre-requisite:

STAT 330 and its core concepts such as joint, marginal and conditional distributions; means, variances, covariances and correlations; distributions of functions of discrete bivariate random variables; and common families of distributions.


Outline:

Assuming the prerequisite background in chapters 1-4 of the book by Casella and Berger, the course will cover:

  1. Review of distributions of functions of continuous bivariate random vectors (sections 2.1, 4.3 of text).
  2. Estimation in finite samples: simple likelihood estimators; judging quality of estimators via MSE and unbiasedness and the use of sufficient statistics and the Rao-Blackwell theorem in this regard.
  3. Testing in finite samples: Constructing likelihood ratio tests (LRTs); optimality of LRTs for point null and alternative hypotheses and the Neyman-Pearson lemma
  4. Interval estimation in finite samples: Inverting test statistics; pivotal quantities
  5. Convergence concepts for estimators: Central limit theorem; Weak Law of Large Numbers (convergence in probability); Slutsky's theorem; Delta-method for obtaining asymptotic distributions of functions of estimators
  6. Large sample approximations to distributions of estimators: Normal approximations, bootstrap
  7. Testing and interval estimation in large samples: LRTs, Wald and Score tests.

Grading

  • Assignments 10%
  • Quiz 15%
  • Midterm 20%
  • Midterm 20%
  • Final Exam 35%

NOTES:

Above grading is subject to change.

Some of the assignments will involve computing in R.

Materials

RECOMMENDED READING:

Recommended Textbook:

Statistical Inference (2nd ed.) by G. Casella and R. L. Berger. Publisher: Chapman and Hall/CRC
ISBN: 978-0-534-24312-8

REQUIRED READING NOTES:

Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.

Department Undergraduate Notes:

Students with Disabilities:
Students requiring accommodations as a result of disability must contact the Centre for Accessible Learning 778-782-3112 or caladmin@sfu.ca.  


Tutor Requests:
Students looking for a tutor should visit https://www.sfu.ca/stat-actsci/all-students/other-resources/tutoring.html. We accept no responsibility for the consequences of any actions taken related to tutors.

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

At SFU, you are expected to act honestly and responsibly in all your academic work. Cheating, plagiarism, or any other form of academic dishonesty harms your own learning, undermines the efforts of your classmates who pursue their studies honestly, and goes against the core values of the university.

To learn more about the academic disciplinary process and relevant academic supports, visit: 


RELIGIOUS ACCOMMODATION

Students with a faith background who may need accommodations during the term are encouraged to assess their needs as soon as possible and review the Multifaith religious accommodations website. The page outlines ways they begin working toward an accommodation and ensure solutions can be reached in a timely fashion.