# Fall 2022 - STAT 450 D100

## Overview

• #### Course Times + Location:

Mo 10:30 AM – 12:20 PM
AQ 5039, Burnaby

We 10:30 AM – 11:20 AM
AQ 5039, Burnaby

• #### Exam Times + Location:

Dec 10, 2022
3:30 PM – 6:30 PM
BLU 10655, 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:

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.

• 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 Textbook:

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

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.

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.