Simon Fraser University
Engaging the World

Course Outlines

Fall 2021 - STAT 450 D100

Statistical Theory (3)

Class Number: 5071

Delivery Method: In Person

Overview

  • Course Times + Location:

    Sep 8 – Dec 7, 2021: Mon, 10:30–11:20 a.m.
    Burnaby

    Sep 8 – Dec 7, 2021: Thu, 10:30 a.m.–12:20 p.m.
    Burnaby

  • Exam Times + Location:

    Dec 15, 2021
    Wed, 7:00–10:00 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 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

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 csdo@sfu.ca


Tutor Requests:
Students looking for a tutor should visit hhttps://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 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

TEACHING AT SFU IN FALL 2021

Teaching at SFU in fall 2021 will involve primarily in-person instruction, with approximately 70 to 80 per cent of classes in person/on campus, with safety plans in place.  Whether your course will be in-person or through remote methods will be clearly identified in the schedule of classes.  You will also know at enrollment whether remote course components will be “live” (synchronous) or at your own pace (asynchronous).

Enrolling in a course acknowledges that you are able to attend in whatever format is required.  You should not enroll in a course that is in-person if you are not able to return to campus, and should be aware that remote study may entail different modes of learning, interaction with your instructor, and ways of getting feedback on your work than may be the case for in-person classes.

Students with hidden or visible disabilities who may need class or exam accommodations, including in the context of remote learning, are advised to register with the SFU Centre for Accessible Learning (caladmin@sfu.ca or 778-782-3112) as early as possible in order to prepare for the fall 2021 term.