Simon Fraser University
Engaging the World

Course Outlines

Fall 2022 - STAT 450 D100

Statistical Theory (3)

Class Number: 4660

Delivery Method: In Person

Overview

  • Course Times + Location:

    Sep 7 – Dec 6, 2022: Mon, 10:30 a.m.–12:20 p.m.
    Burnaby

    Sep 7 – Dec 6, 2022: Wed, 10:30–11:20 a.m.
    Burnaby

  • Exam Times + Location:

    Dec 10, 2022
    Sat, 3:30–6:30 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 text, 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 20%
  • Midterm 30%
  • Final Exam 50%

NOTES:

Above grading is subject to change.

Some of the assignments will involve computing in {\tt R}.

Materials

RECOMMENDED READING:

Recommended Textbook:

Statistical Inference (2nd ed.) by G. Casella and R. L. Berger. Publisher: Cengage
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

SFU’s Academic Integrity website 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