STAT 642
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Probability Theory and Mathematical Statistics 2
Course Description
Introduction to statistical theory; principles of sufficiency and likelihood; point and interval estimation; maximum likelihood; Bayesian inference; hypothesis testing; Neyman-Pearson lemma; likelihood ratio tests; asymptotic results, including delta method; exponential family.
When Taught
Winter
Min
3
Fixed/Max
3
Fixed
3
Fixed
0
Title
Derive Likelihood
Learning Outcome
Derive likelihood ratio tests, Bayesian tests, Wald tests, and score tests
Title
Evaluate Interval Estimators
Learning Outcome
Evaluate interval estimators with respect to size and coverage probabilities using analytical, bookstrap, and other Monte Carlo methods
Title
Find
Learning Outcome
Find sufficient, minimal sufficient, ancillary, and complete statistics
Title
Evaluate Estimators
Learning Outcome
Evaluate estimators using mean squared error, bias, variance, loss functions, and Monte Carlo methods
Title
STAT 642
Learning Outcome
On completing this course, the student will have facility with the concepts of statistical theory fundamental to future work in probability and statistics. The student will be able to:
Title
Use Methods
Learning Outcome
Use method of moments, maximum likelihood, and the Bayesian approach to find estimators
Title
Use Delta Method
Learning Outcome
Use delta method to find asymptotic properties of transformed random variables
Title
Describe Properties
Learning Outcome
Describe asymptotic properties of estimators with respect to consistency, asymptotic normality, and asymptotic efficiency
Title
Find Interval Estimators
Learning Outcome
Find interval estimators by inverting test statistics, using pivotal quantities, and using the Bayesian approach
Title
Evaluate Asymptotic Properties
Learning Outcome
Evaluate asymptotic properties of estimators with respect to consistency, asymptotic normality, and asymptotic efficiency
Title
Apply Theorems
Learning Outcome
Apply the Rao-Blackwell Theorem and Lehmann-Scheffe's Theorem to improve existing estimators
Title
Evaluate Tests
Learning Outcome
Evaluate tests with respect to error probabilities and power using analytical, bookstrap, and other Monte Carlo methods
Title
Find UMP Tests
Learning Outcome
Use the Neyman-Pearson Lemma to find UMP tests
