Statistical Theory

Department: 
MATH
Course Number: 
3236
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
3
Typical Scheduling: 
Spring Semester

This course is an introduction to theoretical statistics for students with a background in probability. A mathematical formalism for inference on experimental data will be developed.

Prerequisites: 

MATH 3235 Introduction to Probability

Course Text: 

M. H. De Groot, Probability and Statistics, 3rd edition

Topic Outline: 

  • Sample sets

  • Parametric statistical inference

  • Point estimation

  • Confidence intervals

  • Estimation Techniques: Method of Moments, Maximum Likelihood Estimation

  • Cramer-Rao Inequality; Asymptotic normality of the MLE

  • Hypothesis Testing; Likelihood Ratio Tests; Chi-Squared Tests

  • Introduction to regression

  • Analysis of Variance

Instructors may cover additional topics including but not restricted to:

  • Topics in Machine Learning such as classification, logistic regression, and Principal Component Analysis

  • Introduction to the statistical software R